text
stringlengths 89
2.49k
| category
stringclasses 19
values |
|---|---|
Ground state of the hard-core Bose gas on lattice I. Energy estimates: We investigate the properties of the ground state of a system of interacting
bosons on regular lattices with coordination number $k\geq 2$. The interaction
is a pure, infinite, on-site repulsion. Our concern is to give an improved
upper bound on the ground state energy per site. For a density $\rho$ a trivial
upper bound is known to be $-k\rho(1-\rho)$. We obtain a smaller variational
bound within a reasonably large family of trial functions. The estimates make
use of a large deviation principle for the energy of the Ising model on the
same lattice. | cond-mat_stat-mech |
Beyond quantum microcanonical statistics: Descriptions of molecular systems usually refer to two distinct theoretical
frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of
an isolated system which is determined to calculate molecular properties and to
consider the time evolution according to the unitary Schr\"odinger equation. On
the other hand a mixed state, i.e. a statistical density matrix, is the
standard formalism to account for thermal equilibrium, as postulated in the
microcanonical quantum statistics. In the present paper an alternative
treatment relying on a statistical analysis of the possible wavefunctions of an
isolated system is presented. In analogy with the classical ergodic theory, the
time evolution of the wavefunction determines the probability distribution in
the phase space pertaining to an isolated system. However, this alone cannot
account for a well defined thermodynamical description of the system in the
macroscopic limit, unless a suitable probability distribution for the quantum
constants of motion is introduced. We present a workable formalism assuring the
emergence of typical values of thermodynamic functions, such as the internal
energy and the entropy, in the large size limit of the system. This allows the
identification of macroscopic properties independently of the specific
realization of the quantum state. A description of material systems in
agreement with equilibrium thermodynamics is then derived without constraints
on the physical constituents and interactions of the system. Furthermore, the
canonical statistics is recovered in all generality for the reduced density
matrix of a subsystem. | cond-mat_stat-mech |
Chains of Viscoelastic Spheres: Given a chain of viscoelastic spheres with fixed masses of the first and last
particles. We raise the question: How to chose the masses of the other
particles of the chain to assure maximal energy transfer? The results are
compared with a chain of particles for which a constant coefficient of
restitution is assumed. Our simple example shows that the assumption of
viscoelastic particle properties has not only important consequences for very
large systems (see [1]) but leads also to qualitative changes in small systems
as compared with particles interacting via a constant restitution coefficient. | cond-mat_stat-mech |
Nonequilibrium statistical mechanics and entropy production in a
classical infinite system of rotators: We analyze the dynamics of a simple but nontrivial classical Hamiltonian
system of infinitely many coupled rotators. We assume that this infinite system
is driven out of thermal equilibrium either because energy is injected by an
external force (Case I), or because heat flows between two thermostats at
different temperatures (Case II). We discuss several possible definitions of
the entropy production associated with a finite or infinite region, or with a
partition of the system into a finite number of pieces. We show that these
definitions satisfy the expected bounds in terms of thermostat temperatures and
energy flow. | cond-mat_stat-mech |
Optimized Monte Carlo Method for glasses: A new Monte Carlo algorithm is introduced for the simulation of supercooled
liquids and glass formers, and tested in two model glasses. The algorithm is
shown to thermalize well below the Mode Coupling temperature and to outperform
other optimized Monte Carlo methods. Using the algorithm, we obtain finite size
effects in the specific heat. This effect points to the existence of a large
correlation length measurable in equal time correlation functions. | cond-mat_stat-mech |
Heat Transport in low-dimensional systems: Recent results on theoretical studies of heat conduction in low-dimensional
systems are presented. These studies are on simple, yet nontrivial, models.
Most of these are classical systems, but some quantum-mechanical work is also
reported. Much of the work has been on lattice models corresponding to phononic
systems, and some on hard particle and hard disc systems. A recently developed
approach, using generalized Langevin equations and phonon Green's functions, is
explained and several applications to harmonic systems are given. For
interacting systems, various analytic approaches based on the Green-Kubo
formula are described, and their predictions are compared with the latest
results from simulation. These results indicate that for momentum-conserving
systems, transport is anomalous in one and two dimensions, and the thermal
conductivity kappa, diverges with system size L, as kappa ~ L^alpha. For one
dimensional interacting systems there is strong numerical evidence for a
universal exponent alpha =1/3, but there is no exact proof for this so far. A
brief discussion of some of the experiments on heat conduction in nanowires and
nanotubes is also given. | cond-mat_stat-mech |
Spontaneous and induced dynamic correlations in glass-formers II: Model
calculations and comparison to numerical simulations: We study in detail the predictions of various theoretical approaches, in
particular mode-coupling theory (MCT) and kinetically constrained models
(KCMs), concerning the time, temperature, and wavevector dependence of
multi-point correlation functions that quantify the strength of both induced
and spontaneous dynamical fluctuations. We also discuss the precise predictions
of MCT concerning the statistical ensemble and microscopic dynamics dependence
of these multi-point correlation functions. These predictions are compared to
simulations of model fragile and strong glass-forming liquids. Overall, MCT
fares quite well in the fragile case, in particular explaining the observed
crucial role of the statistical ensemble and microscopic dynamics, while MCT
predictions do not seem to hold in the strong case. KCMs provide a simplified
framework for understanding how these multi-point correlation functions may
encode dynamic correlations in glassy materials. However, our analysis
highlights important unresolved questions concerning the application of KCMs to
supercooled liquids. | cond-mat_stat-mech |
Non-equilibrium tube length fluctuations of entangled polymers: We investigate the nonequilibrium tube length fluctuations during the
relaxation of an initially stretched, entangled polymer chain. The
time-dependent variance $\sigma^2$ of the tube length follows in the early-time
regime a simple universal power law $\sigma^2 = A \sqrt{t}$ originating in the
diffusive motion of the polymer segments. The amplitude $A$ is calculated
analytically both from standard reptation theory and from an exactly solvable
lattice gas model for reptation and its dependence on the initial and
equilibrium tube length respectively is discussed. The non-universality
suggests the measurement of the fluctuations (e.g. using flourescence
microscopy) as a test for reptation models. | cond-mat_stat-mech |
Leaf-excluded percolation in two and three dimensions: We introduce the \emph{leaf-excluded} percolation model, which corresponds to
independent bond percolation conditioned on the absence of leaves (vertices of
degree one). We study the leaf-excluded model on the square and simple-cubic
lattices via Monte Carlo simulation, using a worm-like algorithm. By studying
wrapping probabilities, we precisely estimate the critical thresholds to be
$0.355\,247\,5(8)$ (square) and $0.185\,022(3)$ (simple-cubic). Our estimates
for the thermal and magnetic exponents are consistent with those for
percolation, implying that the phase transition of the leaf-excluded model
belongs to the standard percolation universality class. | cond-mat_stat-mech |
Identifying Functional Thermodynamics in Autonomous Maxwellian Ratchets: We introduce a family of Maxwellian Demons for which correlations among
information bearing degrees of freedom can be calculated exactly and in compact
analytical form. This allows one to precisely determine Demon functional
thermodynamic operating regimes, when previous methods either misclassify or
simply fail due to approximations they invoke. This reveals that these Demons
are more functional than previous candidates. They too behave either as
engines, lifting a mass against gravity by extracting energy from a single heat
reservoir, or as Landauer erasers, consuming external work to remove
information from a sequence of binary symbols by decreasing their individual
uncertainty. Going beyond these, our Demon exhibits a new functionality that
erases bits not by simply decreasing individual-symbol uncertainty, but by
increasing inter-bit correlations (that is, by adding temporal order) while
increasing single-symbol uncertainty. In all cases, but especially in the new
erasure regime, exactly accounting for informational correlations leads to
tight bounds on Demon performance, expressed as a refined Second Law of
Thermodynamics that relies on the Kolmogorov-Sinai entropy for dynamical
processes and not on changes purely in system configurational entropy, as
previously employed. We rigorously derive the refined Second Law under minimal
assumptions and so it applies quite broadly---for Demons with and without
memory and input sequences that are correlated or not. We note that general
Maxwellian Demons readily violate previously proposed, alternative such bounds,
while the current bound still holds. | cond-mat_stat-mech |
Work fluctuations of self-propelled particles in the phase separated
state: We study the large deviations of the distribution P(W_\tau) of the work
associated with the propulsion of individual active brownian particles in a
time interval \tau, in the region of the phase diagram where macroscopic phase
separation takes place. P(W_\tau) is characterised by two peaks, associated to
particles in the gaseous and in the clusterised phases, and two separate
non-convex branches. Accordingly, the generating function of W_\tau cumulants
displays a double singularity. We discuss the origin of such non-convex
branches in terms of the peculiar dynamics of the system phases, and the
relation between the observation time \tau and the typical persistence times of
the particles in the two phases. | cond-mat_stat-mech |
Quenching along a gapless line: A different exponent for defect density: We use a new quenching scheme to study the dynamics of a one-dimensional
anisotropic $XY$ spin-1/2 chain in the presence of a transverse field which
alternates between the values $h+\de$ and $h-\de$ from site to site. In this
quenching scheme, the parameter denoting the anisotropy of interaction ($\ga$)
is linearly quenched from $-\infty$ to $ +\infty$ as $\ga = t/\tau$, keeping
the total strength of interaction $J$ fixed. The system traverses through a
gapless phase when $\ga$ is quenched along the critical surface $h^2 = \de^2 +
J^2$ in the parameter space spanned by $h$, $\de$ and $\ga$. By mapping to an
equivalent two-level Landau-Zener problem, we show that the defect density in
the final state scales as $1/\tau^{1/3}$, a behavior that has not been observed
in previous studies of quenching through a gapless phase. We also generalize
the model incorporating additional alternations in the anisotropy or in the
strength of the interaction, and derive an identical result under a similar
quenching. Based on the above results, we propose a general scaling of the
defect density with the quenching rate $\tau$ for quenching along a gapless
critical line. | cond-mat_stat-mech |
Dynamics of Rod like Particles in Supercooled Liquids -- Probing Dynamic
Heterogeneity and Amorphous Order: Probing dynamic and static correlation in glass-forming supercooled liquids
has been a challenge for decades in spite of extensive research. Dynamic
correlation which manifests itself as Dynamic Heterogeneity is ubiquitous in a
vast variety of systems starting from molecular glass-forming liquids, dense
colloidal systems to collections of cells. On the other hand, the mere concept
of static correlation in these dense disordered systems remain somewhat elusive
and its existence is still actively debated. We propose a novel method to
extract both dynamic and static correlations using rod-like particles as probe.
This method can be implemented in molecular glass-forming liquids in
experiments as well as in other soft matter systems including biologically
relevant systems. We also rationalize the observed log-normal like distribution
of rotational decorrelation time of elongated probe molecules in reported
experimental studies along with a proposal of a novel methodology to extract
dynamic and static correlation lengths in experiments. | cond-mat_stat-mech |
Iterated Conformal Dynamics and Laplacian Growth: The method of iterated conformal maps for the study of Diffusion Limited
Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and
related processes. We emphasize the fundamental difference between these
processes: DLA is grown serially with constant size particles, while Laplacian
patterns are grown by advancing each boundary point in parallel, proportionally
to the gradient of the Laplacian field. We introduce a 2-parameter family of
growth patterns that interpolates between DLA and a discrete version of
Laplacian growth. The ultraviolet putative finite-time singularities are
regularized here by a minimal tip size, equivalently for all the models in this
family. With this we stress that the difference between DLA and Laplacian
growth is NOT in the manner of ultraviolet regularization, but rather in their
deeply different growth rules. The fractal dimensions of the asymptotic
patterns depend continuously on the two parameters of the family, giving rise
to a "phase diagram" in which DLA and discretized Laplacian growth are at the
extreme ends. In particular we show that the fractal dimension of Laplacian
growth patterns is much higher than the fractal dimension of DLA, with the
possibility of dimension 2 for the former not excluded. | cond-mat_stat-mech |
Path statistics, memory, and coarse-graining of continuous-time random
walks on networks: Continuous-time random walks (CTRWs) on discrete state spaces, ranging from
regular lattices to complex networks, are ubiquitous across physics, chemistry,
and biology. Models with coarse-grained states, for example those employed in
studies of molecular kinetics, and models with spatial disorder can give rise
to memory and non-exponential distributions of waiting times and first-passage
statistics. However, existing methods for analyzing CTRWs on complex energy
landscapes do not address these effects. We therefore use statistical mechanics
of the nonequilibrium path ensemble to characterize first-passage CTRWs on
networks with arbitrary connectivity, energy landscape, and waiting time
distributions. Our approach is valuable for calculating higher moments (beyond
the mean) of path length, time, and action, as well as statistics of any
conservative or non-conservative force along a path. For homogeneous networks
we derive exact relations between length and time moments, quantifying the
validity of approximating a continuous-time process with its discrete-time
projection. For more general models we obtain recursion relations, reminiscent
of transfer matrix and exact enumeration techniques, to efficiently calculate
path statistics numerically. We have implemented our algorithm in PathMAN, a
Python script that users can easily apply to their model of choice. We
demonstrate the algorithm on a few representative examples which underscore the
importance of non-exponential distributions, memory, and coarse-graining in
CTRWs. | cond-mat_stat-mech |
A systematic $1/c$-expansion of form factor sums for dynamical
correlations in the Lieb-Liniger model: We introduce a framework for calculating dynamical correlations in the
Lieb-Liniger model in arbitrary energy eigenstates and for all space and time,
that combines a Lehmann representation with a $1/c$ expansion. The $n^{\rm th}$
term of the expansion is of order $1/c^n$ and takes into account all $\lfloor
\tfrac{n}{2}\rfloor+1$ particle-hole excitations over the averaging eigenstate.
Importantly, in contrast to a 'bare' $1/c$ expansion it is uniform in space and
time. The framework is based on a method for taking the thermodynamic limit of
sums of form factors that exhibit non integrable singularities. We expect our
framework to be applicable to any local operator.
We determine the first three terms of this expansion and obtain an explicit
expression for the density-density dynamical correlations and the dynamical
structure factor at order $1/c^2$. We apply these to finite-temperature
equilibrium states and non-equilibrium steady states after quantum quenches. We
recover predictions of (nonlinear) Luttinger liquid theory and generalized
hydrodynamics in the appropriate limits, and are able to compute sub-leading
corrections to these. | cond-mat_stat-mech |
Folding transitions in three-dimensional space with defects: A model describing the three-dimensional folding of the triangular lattice on
the face-centered cubic lattice is generalized allowing the presence of defects
corresponding to cuts in the two-dimensional network. The model can be
expressed in terms of Ising-like variables with nearest-neighbor and plaquette
interactions in the hexagonal lattice; its phase diagram is determined by the
Cluster Variation Method. The results found by varying the curvature and defect
energy show that the introduction of defects turns the first-order crumpling
transitions of the model without defects into continuous transitions. New
phases also appear by decreasing the energy cost of defects and the behavior of
their densities has been analyzed. | cond-mat_stat-mech |
Exact Markovian kinetic equation for a quantum Brownian oscillator: We derive an exact Markovian kinetic equation for an oscillator linearly
coupled to a heat bath, describing quantum Brownian motion. Our work is based
on the subdynamics formulation developed by Prigogine and collaborators. The
space of distribution functions is decomposed into independent subspaces that
remain invariant under Liouville dynamics. For integrable systems in
Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled,
renormalized particles. In contrast for non-integrable systems, the invariant
subspaces follow a dynamics with broken-time symmetry, involving generalized
functions. This result indicates that irreversibility and stochasticity are
exact properties of dynamics in generalized function spaces. We comment on the
relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation. | cond-mat_stat-mech |
Statistical properties of the laser beam propagating in a turbulent
medium: We examine statistical properties of a laser beam propagating in a turbulent
medium. We prove that the intensity fluctuations at large propagation distances
possess Gaussian probability density function and establish quantitative
criteria for realizing the Gaussian statistics depending on the laser
propagation distance, the laser beam waist, the laser frequency and the
turbulence strength. We calculate explicitly the laser envelope pair
correlation function and corrections to its higher order correlation functions
breaking Gaussianity. We discuss also statistical properties of the brightest
spots in the speckle pattern. | cond-mat_stat-mech |
Preface: Long-range Interactions and Synchronization: Spontaneous synchronization is a general phenomenon in which a large
population of coupled oscillators of diverse natural frequencies self-organize
to operate in unison. The phenomenon occurs in physical and biological systems
over a wide range of spatial and temporal scales, e.g., in electrochemical and
electronic oscillators, Josephson junctions, laser arrays, animal flocking,
pedestrians on footbridges, audience clapping, etc. Besides the obvious
necessity of the synchronous firings of cardiac cells to keep the heart
beating, synchrony is desired in many man-made systems such as parallel
computing, electrical power-grids. On the contrary, synchrony could also be
hazardous, e.g., in neurons, leading to impaired brain function in Parkinson's
disease and epilepsy. Due to this wide range of applications, collective
synchrony in networks of oscillators has attracted the attention of physicists,
applied mathematicians and researchers from many other fields. An essential
aspect of synchronizing systems is that long-range order naturally appear in
these systems, which questions the fact whether long-range interactions may be
particular suitable to synchronization. In this context, it is interesting to
remind that long-range interacting system required several adaptations from
statistical mechanics \`a la Gibbs Boltzmann, in order to deal with the
peculiarities of these systems: negative specific heat, breaking of ergodicity
or lack of extensivity. As for synchrony, it is still lacking a theoretical
framework to use the tools from statistical mechanics. The present issue
presents a collection of exciting recent theoretical developments in the field
of synchronization and long-range interactions, in order to highlight the
mutual progresses of these twin areas. | cond-mat_stat-mech |
Spontaneous cold-to-hot heat transfer in Knudsen gas: It is well known that, when in a thermal bath, a Knudsen gas may reach a
nonequilibrium steady state; often, this is not treated as a thermodynamic
problem. Here, we show that if incorporated in a large-sized setup, such a
phenomenon has nontrivial consequences and cannot circumvent thermodynamics:
cold-to-hot heat transfer may spontaneously occur without an energetic penalty,
either cyclically (with entropy barriers) or continuously (with an energy
barrier). As the system obeys the first law of thermodynamics, the second law
of thermodynamics cannot be applied. | cond-mat_stat-mech |
Mean-Field Approximation for Spacing Distribution Functions in Classical
Systems: We propose a mean-field method to calculate approximately the spacing
distribution functions $p^{(n)}(s)$ in 1D classical many-particle systems. We
compare our method with two other commonly used methods, the independent
interval approximation (IIA) and the extended Wigner surmise (EWS). In our
mean-field approach, $p^{(n)}(s)$ is calculated from a set Langevin equations
which are decoupled by using a mean-field approximation. We found that in spite
of its simplicity, the mean-field approximation provides good results in
several systems. We offer many examples in which the three methods mentioned
previously give a reasonable description of the statistical behavior of the
system. The physical interpretation of each method is also discussed. | cond-mat_stat-mech |
Hyperuniformity of Quasicrystals: Hyperuniform systems, which include crystals, quasicrystals and special
disordered systems, have attracted considerable recent attention, but rigorous
analyses of the hyperuniformity of quasicrystals have been lacking because the
support of the spectral intensity is dense and discontinuous. We employ the
integrated spectral intensity, $Z(k)$, to quantitatively characterize the
hyperuniformity of quasicrystalline point sets generated by projection methods.
The scaling of $Z(k)$ as $k$ tends to zero is computed for one-dimensional
quasicrystals and shown to be consistent with independent calculations of the
variance, $\sigma^2(R)$, in the number of points contained in an interval of
length $2R$. We find that one-dimensional quasicrystals produced by projection
from a two-dimensional lattice onto a line of slope $1/\tau$ fall into distinct
classes determined by the width of the projection window. For a countable dense
set of widths, $Z(k) \sim k^4$; for all others, $Z(k)\sim k^2$. This
distinction suggests that measures of hyperuniformity define new classes of
quasicrystals in higher dimensions as well. | cond-mat_stat-mech |
The effect of memory and active forces on transition path times
distributions: An analytical expression is derived for the transition path time distribution
for a one-dimensional particle crossing of a parabolic barrier. Two cases are
analyzed: (i) A non-Markovian process described by a generalized Langevin
equation with a power-law memory kernel and (ii) a Markovian process with a
noise violating the fluctuation-dissipation theorem, modeling the stochastic
dynamics generated by active forces. In the case (i) we show that the anomalous
dynamics strongly affecting the short time behavior of the distributions, but
this happens only for very rare events not influencing the overall statistics.
At long times the decay is always exponential, in disagreement with a recent
study suggesting a stretched exponential decay. In the case (ii) the active
forces do not substantially modify the short time behavior of the distribution,
but lead to an overall decrease of the average transition path time. These
findings offer some novel insights, useful for the analysis of experiments of
transition path times in (bio)molecular systems. | cond-mat_stat-mech |
Non-Debye relaxations: The characteristic exponent in the excess wings
model: The characteristic (Laplace or L\'evy) exponents uniquely characterize
infinitely divisible probability distributions. Although of purely mathematical
origin they appear to be uniquely associated with the memory functions present
in evolution equations which govern the course of such physical phenomena like
non-Debye relaxations or anomalous diffusion. Commonly accepted procedure to
mimic memory effects is to make basic equations time smeared, i.e., nonlocal in
time. This is modeled either through the convolution of memory functions with
those describing relaxation/diffusion or, alternatively, through the time
smearing of time derivatives. Intuitive expectations say that such introduced
time smearings should be physically equivalent. This leads to the conclusion
that both kinds of so far introduced memory functions form a "twin" structure
familiar to mathematicians for a long time and known as the Sonine pair. As an
illustration of the proposed scheme we consider the excess wings model of
non-Debye relaxations, determine its evolution equations and discuss properties
of the solutions. | cond-mat_stat-mech |
Random Deposition Model with a Constant Capture Length: We introduce a sequential model for the deposition and aggregation of
particles in the submonolayer regime. Once a particle has been randomly
deposited on the substrate, it sticks to the closest atom or island within a
distance \ell, otherwise it sticks to the deposition site. We study this model
both numerically and analytically in one dimension. A clear comprehension of
its statistical properties is provided, thanks to capture equations and to the
analysis of the island-island distance distribution. | cond-mat_stat-mech |
Dimensionality effects in restricted bosonic and fermionic systems: The phenomenon of Bose-like condensation, the continuous change of the
dimensionality of the particle distribution as a consequence of freezing out of
one or more degrees of freedom in the low particle density limit, is
investigated theoretically in the case of closed systems of massive bosons and
fermions, described by general single-particle hamiltonians. This phenomenon is
similar for both types of particles and, for some energy spectra, exhibits
features specific to multiple-step Bose-Einstein condensation, for instance the
appearance of maxima in the specific heat.
In the case of fermions, as the particle density increases, another
phenomenon is also observed. For certain types of single particle hamiltonians,
the specific heat is approaching asymptotically a divergent behavior at zero
temperature, as the Fermi energy $\epsilon_{\rm F}$ is converging towards any
value from an infinite discrete set of energies: ${\epsilon_i}_{i\ge 1}$. If
$\epsilon_{\rm F}=\epsilon_i$, for any i, the specific heat is divergent at T=0
just in infinite systems, whereas for any finite system the specific heat
approaches zero at low enough temperatures. The results are particularized for
particles trapped inside parallelepipedic boxes and harmonic potentials.
PACS numbers: 05.30.Ch, 64.90.+b, 05.30.Fk, 05.30.Jp | cond-mat_stat-mech |
Critical Casimir effects in 2D Ising model with curved defect lines: This work is aimed at studying the influence of critical Casimir effects on
energetic properties of curved defect lines in the frame of 2D Ising model. Two
types of defect curves were investigated. We start with a simple task of
globule formation from four-defect line. It was proved that an exothermic
reaction of collapse occurs and the dependence of energy release on temperature
was observed. Critical Casimir energy of extensive line of constant curvature
was also examined. It was shown that its critical Casimir energy is
proportional to curvature that leads to the tendency to radius decreasing under
Casimir forces. The results obtained can be applied to proteins folding problem
in polarized liquid. | cond-mat_stat-mech |
Velocity and Speed Correlations in Hamiltonian Flocks: We study a $2d$ Hamiltonian fluid made of particles carrying spins coupled to
their velocities. At low temperatures and intermediate densities, this
conservative system exhibits phase coexistence between a collectively moving
droplet and a still gas. The particle displacements within the droplet have
remarkably similar correlations to those of birds flocks. The center of mass
behaves as an effective self-propelled particle, driven by the droplet's total
magnetization. The conservation of a generalized angular momentum leads to
rigid rotations, opposite to the fluctuations of the magnetization orientation
that, however small, are responsible for the shape and scaling of the
correlations. | cond-mat_stat-mech |
Universal dimensional crossover of domain wall dynamics in ferromagnetic
films: The magnetic domain wall motion driven by a magnetic field is studied in
(Ga,Mn)As and (Ga,Mn)(As,P) films of different thicknesses. In the thermally
activated creep regime, a kink in the velocity curves and a jump of the
roughness exponent evidence a dimensional crossover in the domain wall
dynamics. The measured values of the roughness exponent zeta_{1d} = 0.62 +/-
0.02 and zeta_{2d} = 0.45 +/- 0.04 are compatible with theoretical predictions
for the motion of elastic line (d = 1) and surface (d = 2) in two and three
dimensional media, respectively. | cond-mat_stat-mech |
Master equation approach to the stochastic accumulation dynamics of
bacterial cell cycle: The mechanism of bacterial cell size control has been a mystery for decades,
which involves the well-coordinated growth and division in the cell cycle. The
revolutionary modern techniques of microfluidics and the advanced live imaging
analysis techniques allow long term observations and high-throughput analysis
of bacterial growth on single cell level, promoting a new wave of quantitative
investigations on this puzzle. Taking the opportunity, this theoretical study
aims to clarify the stochastic nature of bacterial cell size control under the
assumption of the accumulation mechanism, which is favoured by recent
experiments on species of bacteria. Via the master equation approach with
properly chosen boundary conditions, the distributions concerned in cell size
control are estimated and are confirmed by experiments. In this analysis, the
inter-generation Green's function is analytically evaluated as the key to
bridge two kinds of statistics used in batch-culture and mother machine
experiments. This framework allows us to quantify the noise level in growth and
accumulation according to experimental data. As a consequence of non-Gaussian
noises of the added sizes, the non-equilibrium nature of bacterial cell size
homeostasis is predicted, of which the biological meaning requires further
investigation. | cond-mat_stat-mech |
The asymptotic Bethe ansatz solution for one-dimensional SU(2) spinor
bosons with finite range Gaussian interactions: We propose a one-dimensional model of spinor bosons with SU(2) symmetry and a
two-body finite range Gaussian interaction potential. We show that the model is
exactly solvable when the width of the interaction potential is much smaller
compared to the inter-particle separation. This model is then solved via the
asymptotic Bethe ansatz technique. The ferromagnetic ground state energy and
chemical potential are derived analytically. We also investigate the effects of
a finite range potential on the density profiles through local density
approximation. Finite range potentials are more likely to lead to quasi
Bose-Einstein condensation than zero range potentials. | cond-mat_stat-mech |
Critical behavior of the Coulomb-glass model in the zero-disorder limit:
Ising universality in a system with long-range interactions: The ordering of charges on half-filled hypercubic lattices is investigated
numerically, where electroneutrality is ensured by background charges. This
system is equivalent to the $s = 1/2$ Ising lattice model with
antiferromagnetic $1/r$ interaction. The temperature dependences of specific
heat, mean staggered occupation, and of a generalized susceptibility indicate
continuous order-disorder phase transitions at finite temperatures in two- and
three-dimensional systems. In contrast, the susceptibility of the
one-dimensional system exhibits singular behavior at vanishing temperature. For
the two- and three-dimensional cases, the critical exponents are obtained by
means of a finite-size scaling analysis. Their values are consistent with those
of the Ising model with short-range interaction, and they imply that the
studied model cannot belong to any other known universality class. Samples of
up to 1400, $112^2$, and $22^3$ sites are considered for dimensions 1 to 3,
respectively. | cond-mat_stat-mech |
Reply to Comment on Effect of polydispersity on the ordering transition
of adsorbed self-assembled rigid rods: We comment on the nature of the ordering transition of a model of equilibrium
polydisperse rigid rods, on the square lattice, which is reported by Lopez et
al. to exhibit random percolation criticality in the canonical ensemble, in
sharp contrast to (i) our results of Ising criticality for the same model in
the grand canonical ensemble [Phys. Rev. E 82, 061117 (2010)] and (ii) the
absence of exponent(s) renormalization for constrained systems with logarithmic
specific heat anomalies predicted on very general grounds by Fisher [M.E.
Fisher, Phys. Rev. 176, 257 (1968)]. | cond-mat_stat-mech |
Percolation of sticks: effect of stick alignment and length dispersity: Using Monte Carlo simulation, we studied the percolation of sticks, i.e.
zero-width rods, on a plane paying special attention to the effects of stick
alignment and their length dispersity. The stick lengths were distributed in
accordance with log-normal distributions, providing a constant mean length with
different widths of distribution. Scaling analysis was performed to obtain the
percolation thresholds in the thermodynamic limits for all values of the
parameters. Greater alignment of the sticks led to increases in the percolation
threshold while an increase in length dispersity decreased the percolation
threshold. A fitting formula has been proposed for the dependency of the
percolation threshold both on stick alignment and on length dispersity. | cond-mat_stat-mech |
Supercooled liquids are Fickian yet non-Gaussian: Reply to "Comment on 'Fickian non-Gaussian diffusion in glass-forming
liquids' ".
In [ArXiv:2210.07119v1], Berthier et al. questioned the findings of our
letter [Phys. Rev. Lett. 128, 168001 (2022)], concerning the existence and the
features of Fickian non-Gaussian diffusion in glass-forming liquids. Here we
demonstrate that their arguments are either wrong, or not meaningful to our
scope. Thus, we fully confirm the validity and novelty of our results. | cond-mat_stat-mech |
Velocity Distributions in Homogeneously Cooling and Heated Granular
Fluids: We study the single particle velocity distribution for a granular fluid of
inelastic hard spheres or disks, using the Enskog-Boltzmann equation, both for
the homogeneous cooling of a freely evolving system and for the stationary
state of a uniformly heated system, and explicitly calculate the fourth
cumulant of the distribution. For the undriven case, our result agrees well
with computer simulations of Brey et al. \cite{brey}. Corrections due to
non-Gaussian behavior on cooling rate and stationary temperature are found to
be small at all inelasticities. The velocity distribution in the uniformly
heated steady state exhibits a high energy tail $\sim \exp(-A c^{3/2})$, where
$c$ is the velocity scaled by the thermal velocity and $A\sim 1/\sqrt{\eps}$
with $\eps$ the inelasticity. | cond-mat_stat-mech |
Modified Thirring model beyond the excluded-volume approximation: Long-range interacting systems may exhibit ensemble inequivalence and can
possibly attain equilibrium states under completely open conditions, for which
energy, volume and number of particles simultaneously fluctuate. Here we
consider a modified version of the Thirring model for self-gravitating systems
with attractive and repulsive long-range interactions in which particles are
treated as hard spheres in dimension d=1,2,3. Equilibrium states of the model
are studied under completely open conditions, in the unconstrained ensemble, by
means of both Monte Carlo simulations and analytical methods and are compared
with the corresponding states at fixed number of particles, in the
isothermal-isobaric ensemble. Our theoretical description is performed for an
arbitrary local equation of state, which allows us to examine the system beyond
the excluded-volume approximation. The simulations confirm the theoretical
prediction of the possible occurrence of first-order phase transitions in the
unconstrained ensemble. This work contributes to the understanding of
long-range interacting systems exchanging heat, work and matter with the
environment. | cond-mat_stat-mech |
Microscopic View on Short-Range Wetting at the Free Surface of the
Binary Metallic Liquid Gallium-Bismuth: An X-ray Reflectivity and Square
Gradient Theory Study: We present an x-ray reflectivity study of wetting at the free surface of the
binary liquid metal gallium-bismuth (Ga-Bi) in the region where the bulk phase
separates into Bi-rich and Ga-rich liquid phases. The measurements reveal the
evolution of the microscopic structure of wetting films of the Bi-rich,
low-surface-tension phase along different paths in the bulk phase diagram. A
balance between the surface potential preferring the Bi-rich phase and the
gravitational potential which favors the Ga-rich phase at the surface pins the
interface of the two demixed liquid metallic phases close to the free surface.
This enables us to resolve it on an Angstrom level and to apply a mean-field,
square gradient model extended by thermally activated capillary waves as
dominant thermal fluctuations. The sole free parameter of the gradient model,
i.e. the so-called influence parameter, $\kappa$, is determined from our
measurements. Relying on a calculation of the liquid/liquid interfacial tension
that makes it possible to distinguish between intrinsic and capillary wave
contributions to the interfacial structure we estimate that fluctuations affect
the observed short-range, complete wetting phenomena only marginally. A
critical wetting transition that should be sensitive to thermal fluctuations
seems to be absent in this binary metallic alloy. | cond-mat_stat-mech |
Learning nonequilibrium control forces to characterize dynamical phase
transitions: Sampling the collective, dynamical fluctuations that lead to nonequilibrium
pattern formation requires probing rare regions of trajectory space. Recent
approaches to this problem based on importance sampling, cloning, and spectral
approximations, have yielded significant insight into nonequilibrium systems,
but tend to scale poorly with the size of the system, especially near dynamical
phase transitions. Here we propose a machine learning algorithm that samples
rare trajectories and estimates the associated large deviation functions using
a many-body control force by leveraging the flexible function representation
provided by deep neural networks, importance sampling in trajectory space, and
stochastic optimal control theory. We show that this approach scales to
hundreds of interacting particles and remains robust at dynamical phase
transitions. | cond-mat_stat-mech |
Stationary State Skewness in Two Dimensional KPZ Type Growth: We present numerical Monte Carlo results for the stationary state properties
of KPZ type growth in two dimensional surfaces, by evaluating the finite size
scaling (FSS) behaviour of the 2nd and 4th moments, $W_2$ and $W_4$, and the
skewness, $W_3$, in the Kim-Kosterlitz (KK) and BCSOS model. Our results agree
with the stationary state proposed by L\"assig. The roughness exponents
$W_n\sim L^{\alpha_n}$ obey power counting, $\alpha_n= n \alpha$, and the
amplitude ratio's of the moments are universal. They have the same values in
both models: $W_3/W_2^{1.5}= -0.27(1)$ and $W_4/W_2^{2}= +3.15(2)$. Unlike in
one dimension, the stationary state skewness is not tunable, but a universal
property of the stationary state distribution. The FSS corrections to scaling
in the KK model are weak and $\alpha$ converges well to the
Kim-Kosterlitz-L\"assig value $\alpha={2/5} $. The FSS corrections to scaling
in the BCSOS model are strong. Naive extrapolations yield an smaller value,
$\alpha\simeq 0.38(1)$, but are still consistent with $\alpha={2/5}$ if the
leading irrelevant corrections to FSS scaling exponent is of order
$y_{ir}\simeq -0.6(2)$. | cond-mat_stat-mech |
Properties of Higher-Order Phase Transitions: Experimental evidence for the existence of strictly higher-order phase
transitions (of order three or above in the Ehrenfest sense) is tenuous at
best. However, there is no known physical reason why such transitions should
not exist in nature. Here, higher-order transitions characterized by both
discontinuities and divergences are analysed through the medium of partition
function zeros. Properties of the distributions of zeros are derived, certain
scaling relations are recovered, and new ones are presented. | cond-mat_stat-mech |
Percolation in random environment: We consider bond percolation on the square lattice with perfectly correlated
random probabilities. According to scaling considerations, mapping to a random
walk problem and the results of Monte Carlo simulations the critical behavior
of the system with varying degree of disorder is governed by new, random fixed
points with anisotropic scaling properties. For weaker disorder both the
magnetization and the anisotropy exponents are non-universal, whereas for
strong enough disorder the system scales into an {\it infinite randomness fixed
point} in which the critical exponents are exactly known. | cond-mat_stat-mech |
Dynamical systems on large networks with predator-prey interactions are
stable and exhibit oscillations: We analyse the stability of linear dynamical systems defined on sparse,
random graphs with predator-prey, competitive, and mutualistic interactions.
These systems are aimed at modelling the stability of fixed points in large
systems defined on complex networks, such as, ecosystems consisting of a large
number of species that interact through a food-web. We develop an exact theory
for the spectral distribution and the leading eigenvalue of the corresponding
sparse Jacobian matrices. This theory reveals that the nature of local
interactions have a strong influence on system's stability. We show that, in
general, linear dynamical systems defined on random graphs with a prescribed
degree distribution of unbounded support are unstable if they are large enough,
implying a tradeoff between stability and diversity. Remarkably, in contrast to
the generic case, antagonistic systems that only contain interactions of the
predator-prey type can be stable in the infinite size limit. This qualitatively
feature for antagonistic systems is accompanied by a peculiar oscillatory
behaviour of the dynamical response of the system after a perturbation, when
the mean degree of the graph is small enough. Moreover, for antagonistic
systems we also find that there exist a dynamical phase transition and critical
mean degree above which the response becomes non-oscillatory. | cond-mat_stat-mech |
Domino effect for world market fluctuations: In order to emphasize cross-correlations for fluctuations in major market
places, series of up and down spins are built from financial data. Patterns
frequencies are measured, and statistical tests performed. Strong
cross-correlations are emphasized, proving that market moves are collective
behaviors. | cond-mat_stat-mech |
Physics-informed Bayesian inference of external potentials in classical
density-functional theory: The swift progression of machine learning (ML) has not gone unnoticed in the
realm of statistical mechanics. ML techniques have attracted attention by the
classical density-functional theory (DFT) community, as they enable discovery
of free-energy functionals to determine the equilibrium-density profile of a
many-particle system. Within DFT, the external potential accounts for the
interaction of the many-particle system with an external field, thus, affecting
the density distribution. In this context, we introduce a statistical-learning
framework to infer the external potential exerted on a many-particle system. We
combine a Bayesian inference approach with the classical DFT apparatus to
reconstruct the external potential, yielding a probabilistic description of the
external potential functional form with inherent uncertainty quantification.
Our framework is exemplified with a grand-canonical one-dimensional particle
ensemble with excluded volume interactions in a confined geometry. The required
training dataset is generated using a Monte Carlo (MC) simulation where the
external potential is applied to the grand-canonical ensemble. The resulting
particle coordinates from the MC simulation are fed into the learning framework
to uncover the external potential. This eventually allows us to compute the
equilibrium density profile of the system by using the tools of DFT. Our
approach benchmarks the inferred density against the exact one calculated
through the DFT formulation with the true external potential. The proposed
Bayesian procedure accurately infers the external potential and the density
profile. We also highlight the external-potential uncertainty quantification
conditioned on the amount of available simulated data. The seemingly simple
case study introduced in this work might serve as a prototype for studying a
wide variety of applications, including adsorption and capillarity. | cond-mat_stat-mech |
Simulation of heat transport in low-dimensional oscillator lattices: The study of heat transport in low-dimensional oscillator lattices presents a
formidable challenge. Theoretical efforts have been made trying to reveal the
underlying mechanism of diversified heat transport behaviors. In lack of a
unified rigorous treatment, approximate theories often may embody controversial
predictions. It is therefore of ultimate importance that one can rely on
numerical simulations in the investigation of heat transfer processes in
low-dimensional lattices. The simulation of heat transport using the
non-equilibrium heat bath method and the Green-Kubo method will be introduced.
It is found that one-dimensional (1D), two-dimensional (2D) and
three-dimensional (3D) momentum-conserving nonlinear lattices display power-law
divergent, logarithmic divergent and constant thermal conductivities,
respectively. Next, a novel diffusion method is also introduced. The heat
diffusion theory connects the energy diffusion and heat conduction in a
straightforward manner. This enables one to use the diffusion method to
investigate the objective of heat transport. In addition, it contains
fundamental information about the heat transport process which cannot readily
be gathered otherwise. | cond-mat_stat-mech |
Phase diagrams and critical behavior of the quantum spin-1/2 XXZ model
on diamond-type hierarchical lattices: In this paper, the phase diagrams and the critical behavior of the spin-1/2
anisotropic XXZ ferromagnetic model (the anisotropic parameter
{\Delta}\in(-\infty,1]) on two kinds of diamond-type hierarchical (DH) lattices
with fractal dimensions d_{f}=2.58 and 3, respectively, are studied via the
real-space renormalization group method. It is found that in the isotropic
Heisenberg limit ({\Delta}=0), there exist finite temperature phase transitions
for the two kinds of DH lattices above. The systems are also investigated in
the range of -\infty<{\Delta}<0 and it is found that they exhibit XY-like fixed
points. Meanwhile, the critical exponents of the above two systems are also
calculated. The results show that for the lattice with d_{f}=2.58, the value of
the Ising critical exponent {\nu}_{I} is the same as that of classical Ising
model and the isotropic Heisenberg critical exponent {\nu}_{H} is a finite
value, and for the lattice with d_{f}=3, the values of {\nu}_{I} and {\nu}_{H}
agree well with those obtained on the simple cubic lattice. We also discuss the
quantum fluctuation at all temperatures and find the fluctuation of XY-like
model is stronger than the anistropic Heisenberg model at the low-temperature
region. By analyzing the fluctuation, we conclude that there will be remarkable
effect of neglecting terms on the final results of the XY-like model. However,
we can obtain approximate result at bigger temperatures and give qualitatively
correct picture of the phase diagram. | cond-mat_stat-mech |
Hybrid soft-mode and off-center Ti model of barium titanate: It has been recently established by NMR techniques that in the high
temperature cubic phase of BaTiO$_3$ the Ti ions are not confined to the high
symmetry cubic sites, but rather occupy one of the eight off-center positions
along the $[111]$ directions. The off-center Ti picture is in apparent contrast
with most soft-mode type theoretical descriptions of this classical perovskite
ferroelectric. Here we apply a mesoscopic model of BaTiO$_3$, assuming that the
symmetrized occupation operators for the Ti off-center sites are linearly
coupled to the normal coordinates for lattice vibrations. On the time scale of
Ti intersite jumps, most phonon modes are fast and thus merely contribute to an
effective static Ti-Ti interaction. Close to the stability limit for the soft
TO optic modes, however, the phonon time scale becomes comparable to the
relaxation time for the Ti occupational states of $T_{1u}$ symmetry, and a
hybrid vibrational-orientational soft mode appears. The frequency of the hybrid
soft mode is calculated as a function of temperature and coupling strength, and
its its role in the ferroelectric phase transition is discussed. | cond-mat_stat-mech |
Unequal Intra-layer Coupling in a Bilayer Driven Lattice Gas: The system under study is a twin-layered square lattice gas at half-filling,
being driven to non-equilibrium steady states by a large, finite `electric'
field. By making intra-layer couplings unequal we were able to extend the phase
diagram obtained by Hill, Zia and Schmittmann (1996) and found that the
tri-critical point, which separates the phase regions of the stripped (S) phase
(stable at positive interlayer interactions J_3), the filled-empty (FE) phase
(stable at negative J_3) and disorder (D), is shifted even further into the
negative J_3 region as the coupling traverse to the driving field increases.
Many transient phases to the S phase at the S-FE boundary were found to be
long-lived. We also attempted to test whether the universality class of D-FE
transitions under a drive is still Ising. Simulation results suggest a value of
1.75 for the exponent gamma but a value close to 2.0 for the ratio gamma/nu. We
speculate that the D-FE second order transition is different from Ising near
criticality, where observed first-order-like transitions between FE and its
"local minimum" cousin occur during each simulation run. | cond-mat_stat-mech |
Effect of Elastic Deformations on the Critical Behavior of Disordered
Systems with Long-Range Interactions: A field-theoretic approach is applied to describe behavior of
three-dimensional, weakly disordered, elastically isotropic, compressible
systems with long-range interactions at various values of a long-range
interaction parameter. Renormalization-group equations are analyzed in the
two-loop approximation by using the Pade-Borel summation technique. The fixed
points corresponding to critical and tricritical behavior of the systems are
determined. Elastic deformations are shown to changes in critical and
tricritical behavior of disordered compressible systems with long-range
interactions. The critical exponents characterizing a system in the critical
and tricritical regions are determined. | cond-mat_stat-mech |
Comment on "Fluctuation Theorem Uncertainty Relation" and "Thermodynamic
Uncertainty Relations from Exchange Fluctuation Theorems": In recent letter [Phys.~Rev.~Lett {\bf 123}, 110602 (2019)], Y.~Hasegawa and
T.~V.~Vu derived a thermodynamic uncertainty relation. But the bound of their
relation is loose. In this comment, through minor changes, an improved bound is
obtained. This improved bound is the same as the one obtained in
[Phys.~Rev.~Lett {\bf 123}, 090604 (2019)] by A.~M.~Timpanaro {\it et. al.},
but the derivation here is straightforward. | cond-mat_stat-mech |
Screening of an electrically charged particle in a two-dimensional
two-component plasma at $Γ=2$: We consider the thermodynamic effects of an electrically charged impurity
immersed in a two-dimensional two-component plasma, composed by particles with
charges $\pm e$, at temperature $T$, at coupling $\Gamma=e^2/(k_B T)=2$,
confined in a large disk of radius $R$. Particularly, we focus on the analysis
of the charge density, the correlation functions, and the grand potential. Our
analytical results show how the charges are redistributed in the circular
geometry considered here. When we consider a positively charged impurity, the
negative ions accumulate close to the impurity leaving an excess of positive
charge that accumulates at the boundary of the disk. Due to the symmetry under
charge exchange, the opposite effect takes place when we place a negative
impurity. Both the cases in which the impurity charge is an integer multiple of
the particle charges in the plasma, $\pm e$, and a fraction of them are
considered; both situations require a slightly different mathematical
treatments, showing the effect of the quantization of plasma charges. The bulk
and tension effects in the plasma described by the grand potential are not
modified by the introduction of the charged particle. Besides the effects due
to the collapse coming from the attraction between oppositely charged ions, an
additional topological term appears in the grand potential, proportional to
$-n^2\ln(mR)$, with $n$ the dimensionless charge of the particle. This term
modifies the central charge of the system, from $c=1$ to $c=1-6n^2$, when
considered in the context of conformal field theories. | cond-mat_stat-mech |
Emergent non-Hermitian physics in generalized Lotka-Volterra model: In this paper, we study the non-Hermitian physics emerging from a
predator-prey ecological model described by a generalized Lotka-Volterra
equation. In the phase space, this nonlinear equation exhibits both chaotic and
localized dynamics, which are separated by a critical point. These distinct
dynamics originate from the interplay between the periodicity and
non-Hermiticity of the effective Hamiltonian in the linearized equation of
motion. Moreover, the dynamics at the critical point, such as algebraic
divergence, can be understood as an exceptional point in the context of
non-Hermitian physics. | cond-mat_stat-mech |
Identification of a polymer growth process with an equilibrium
multi-critical collapse phase transition: the meeting point of swollen,
collapsed and crystalline polymers: We have investigated a polymer growth process on the triangular lattice where
the configurations produced are self-avoiding trails. We show that the scaling
behaviour of this process is similar to the analogous process on the square
lattice. However, while the square lattice process maps to the collapse
transition of the canonical interacting self-avoiding trail model (ISAT) on
that lattice, the process on the triangular lattice model does not map to the
canonical equilibrium model. On the other hand, we show that the collapse
transition of the canonical ISAT model on the triangular lattice behaves in a
way reminiscent of the $\theta$-point of the interacting self-avoiding walk
model (ISAW), which is the standard model of polymer collapse. This implies an
unusual lattice dependency of the ISAT collapse transition in two dimensions.
By studying an extended ISAT model, we demonstrate that the growth process
maps to a multi-critical point in a larger parameter space. In this extended
parameter space the collapse phase transition may be either $\theta$-point-like
(second-order) or first-order, and these two are separated by a multi-critical
point. It is this multi-critical point to which the growth process maps.
Furthermore, we provide evidence that in addition to the high-temperature
gas-like swollen polymer phase (coil) and the low-temperature liquid drop-like
collapse phase (globule) there is also a maximally dense crystal-like phase
(crystal) at low temperatures dependent on the parameter values. The
multi-critical point is the meeting point of these three phases. Our
hypothesised phase diagram resolves the mystery of the seemingly differing
behaviours of the ISAW and ISAT models in two dimensions as well as the
behaviour of the trail growth process. | cond-mat_stat-mech |
Inequalities generalizing the second law of thermodynamics for
transitions between non-stationary states: We discuss the consequences of a variant of the Hatano-Sasa relation in which
a non-stationary distribution is used in place of the usual stationary one. We
first show that this non-stationary distribution is related to a difference of
traffic between the direct and dual dynamics. With this formalism, we extend
the definition of the adiabatic and non-adiabatic entropies introduced by M.
Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the
stationary case. We also obtain interesting second-law like inequalities for
transitions between non-stationary states. | cond-mat_stat-mech |
Interaction-disorder competition in a spin system evaluated through the
Loschmidt Echo: The interplay between interactions and disorder in closed quantum many-body
systems is relevant for thermalization phenomenon. In this article, we address
this competition in an infinite temperature spin system, by means of the
Loschmidt echo (LE), which is based on a time reversal procedure. This quantity
has been formerly employed to connect quantum and classical chaos, and in the
present many-body scenario we use it as a dynamical witness. We assess the LE
time scales as a function of disorder and interaction strengths. The strategy
enables a qualitative phase diagram that shows the regions of ergodic and
nonergodic behavior of the polarization under the echo dynamics. | cond-mat_stat-mech |
A field-theoretic approach to nonequilibrium work identities: We study nonequilibrium work relations for a space-dependent field with
stochastic dynamics (Model A). Jarzynski's equality is obtained through
symmetries of the dynamical action in the path integral representation. We
derive a set of exact identities that generalize the fluctuation-dissipation
relations to non-stationary and far-from-equilibrium situations. These
identities are prone to experimental verification. Furthermore, we show that a
well-studied invariance of the Langevin equation under supersymmetry, which is
known to be broken when the external potential is time-dependent, can be
partially restored by adding to the action a term which is precisely
Jarzynski's work. The work identities can then be retrieved as consequences of
the associated Ward-Takahashi identities. | cond-mat_stat-mech |
Finite temperature theory of the trapped two dimensional Bose gas: We present a Hartree-Fock-Bogoliubov (HFB) theoretical treatment of the
two-dimensional trapped Bose gas and indicate how semiclassical approximations
to this and other formalisms have lead to confusion. We numerically obtain
results for the fully quantum mechanical HFB theory within the Popov
approximation and show that the presence of the trap stabilizes the condensate
against long wavelength fluctuations. These results are used to show where
phase fluctuations lead to the formation of a quasicondensate. | cond-mat_stat-mech |
Criticality of natural absorbing states: We study a recently introduced ladder model which undergoes a transition
between an active and an infinitely degenerate absorbing phase. In some cases
the critical behaviour of the model is the same as that of the branching
annihilating random walk with $N\geq 2$ species both with and without hard-core
interaction. We show that certain static characteristics of the so-called
natural absorbing states develop power law singularities which signal the
approach of the critical point. These results are also explained using random
walk arguments. In addition to that we show that when dynamics of our model is
considered as a minimum finding procedure, it has the best efficiency very
close to the critical point. | cond-mat_stat-mech |
Uncovering the secrets of the 2d random-bond Blume-Capel model: The effects of bond randomness on the ground-state structure, phase diagram
and critical behavior of the square lattice ferromagnetic Blume-Capel (BC)
model are discussed. The calculation of ground states at strong disorder and
large values of the crystal field is carried out by mapping the system onto a
network and we search for a minimum cut by a maximum flow method. In finite
temperatures the system is studied by an efficient two-stage Wang-Landau (WL)
method for several values of the crystal field, including both the first- and
second-order phase transition regimes of the pure model. We attempt to explain
the enhancement of ferromagnetic order and we discuss the critical behavior of
the random-bond model. Our results provide evidence for a strong violation of
universality along the second-order phase transition line of the random-bond
version. | cond-mat_stat-mech |
A generalized thermodynamics for power-law statistics: We show that there exists a natural way to define a condition of generalized
thermal equilibrium between systems governed by Tsallis thermostatistics, under
the hypotheses that i) the coupling between the systems is weak, ii) the
structure functions of the systems have a power-law dependence on the energy.
It is found that the q values of two such systems at equilibrium must satisfy a
relationship involving the respective numbers of degrees of freedom. The
physical properties of a Tsallis distribution can be conveniently characterized
by a new parameter eta which can vary between 0 and + infinite, these limits
corresponding respectively to the two opposite situations of a microcanonical
distribution and of a distribution with a predominant power-tail at high
energies. We prove that the statistical expression of the thermodynamic
functions is univocally determined by the requirements that a) systems at
thermal equilibrium have the same temperature, b) the definitions of
temperature and entropy are consistent with the second law of thermodynamics.
We find that, for systems satisfying the hypotheses i) and ii) specified above,
the thermodynamic entropy is given by Renyi entropy. | cond-mat_stat-mech |
Directed transport in equilibrium : analysis of the dimer model with
inertial terms: We have previously shown an analysis of our dimer model in the over-damped
regime to show directed transport in equilibrium. Here we analyze the full
model with inertial terms present to establish the same result. First we derive
the Fokker-Planck equation for the system following a Galilean transformation
to show that a uniformly translating equilibrium distribution is possible.
Then, we find out the velocity selection for the centre of mass motion using
that distribution on our model. We suggest generalization of our calculations
for soft collision potentials and indicate to interesting situation with
possibility of oscillatory non-equilibrium state within equilibrium. | cond-mat_stat-mech |
Finite-temperature properties of quasi-2D Bose-Einstein condensates: Using the finite-temperature path integral Monte Carlo method, we investigate
dilute, trapped Bose gases in a quasi-two dimensional geometry. The quantum
particles have short-range, s-wave interactions described by a hard-sphere
potential whose core radius equals its corresponding scattering length. The
effect of both the temperature and the interparticle interaction on the
equilibrium properties such as the total energy, the density profile, and the
superfluid fraction is discussed. We compare our accurate results with both the
semi-classical approximation and the exact results of an ideal Bose gas. Our
results show that for repulsive interactions, (i) the minimum value of the
aspect ratio, where the system starts to behave quasi-two dimensionally,
increases as the two-body interaction strength increases, (ii) the superfluid
fraction for a quasi-2D Bose gas is distinctly different from that for both a
quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a
quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true
3D system with increasing temperature, and shows a stronger dependence on the
interaction strength, (iii) the superfluid fraction for a quasi-2D Bose gas
lies well below the values calculated from the semi-classical approximation,
and (iv) the Kosterlitz-Thouless transition temperature decreases as the
strength of the interaction increases. | cond-mat_stat-mech |
Finite size induced phenomena in 2D classical spin models: We make a short overview of the recent analytic and numerical studies of the
classical two-dimensional XY and Heisenberg models at low temperatures. Special
attention is being paid to an influence of finite system size L on the
peculiarities of the low-temperature phase. In accordance with the
Mermin-Wagner-Hohenberg theorem, spontaneous magnetisation does not appear in
the above models at infinite L. However it emerges for the finite system sizes
and leads to new features of the low-temperature behaviour. | cond-mat_stat-mech |
Quench dynamics and scaling laws in topological nodal loop semimetals: We employ quench dynamics as an effective tool to probe different
universality classes of topological phase transitions. Specifically, we study a
model encompassing both Dirac-like and nodal loop criticalities. Examining the
Kibble-Zurek scaling of topological defect density, we discover that the
scaling exponent is reduced in the presence of extended nodal loop gap
closures. For a quench through a multicritical point, we also unveil a
path-dependent crossover between two sets of critical exponents. Bloch state
tomography finally reveals additional differences in the defect trajectories
for sudden quenches. While the Dirac transition permits a static trajectory
under specific initial conditions, we find that the underlying nodal loop leads
to complex time-dependent trajectories in general. In the presence of a nodal
loop, we find, generically, a mismatch between the momentum modes where
topological defects are generated and where dynamical quantum phase transitions
occur. We also find notable exceptions where this correspondence breaks down
completely. | cond-mat_stat-mech |
Zero temperature coarsening in Ising model with asymmetric second
neighbour interaction in two dimensions: We consider the zero temperature coarsening in the Ising model in two
dimensions where the spins interact within the Moore neighbourhood. The
Hamiltonian is given by $H = - \sum_{<i,j>}{S_iS_j} - \kappa
\sum_{<i,j'>}{S_iS_{j'}}$ where the two terms are for the first neighbours and
second neighbours respectively and $\kappa \geq 0$. The freezing phenomena,
already noted in two dimensions for $\kappa=0$, is seen to be present for any
$\kappa$. However, the frozen states show more complicated structure as
$\kappa$ is increased; e.g. local anti-ferromagnetic motifs can exist for
$\kappa>2$. Finite sized systems also show the existence of an iso-energetic
active phase for $\kappa > 2$, which vanishes in the thermodynamic limit. The
persistence probability shows universal behaviour for $\kappa>0$, however it is
clearly different from the $\kappa=0$ results when non-homogeneous initial
condition is considered. Exit probability shows universal behaviour for all
$\kappa \geq 0$. The results are compared with other models in two dimensions
having interactions beyond the first neighbour. | cond-mat_stat-mech |
Correlation Matrix Spectra: A Tool for Detecting Non-apparent
Correlations?: It has been shown that, if a model displays long-range (power-law) spatial
correlations, its equal-time correlation matrix of this model will also have a
power law tail in the distribution of its high-lying eigenvalues. The purpose
of this letter is to show that the converse is generally incorrect: a power-law
tail in the high-lying eigenvalues of the correlation matrix may exist even in
the absence of equal-time power law correlations in the original model. We may
therefore view the study of the eigenvalue distribution of the correlation
matrix as a more powerful tool than the study of correlations, one which may in
fact uncover structure, that would otherwise not be apparent. Specifically, we
show that in the Totally Asymmetric Simple Exclusion Process, whereas there are
no clearly visible correlations in the steady state, the eigenvalues of its
correlation matrix exhibit a rich structure which we describe in detail. | cond-mat_stat-mech |
Resetting with stochastic return through linear confining potential: We consider motion of an overdamped Brownian particle subject to stochastic
resetting in one dimension. In contrast to the usual setting where the particle
is instantaneously reset to a preferred location (say, the origin), here we
consider a finite time resetting process facilitated by an external linear
potential $V(x)=\lambda|x|~ (\lambda>0)$. When resetting occurs, the trap is
switched on and the particle experiences a force $-\partial_x V(x)$ which helps
the particle to return to the resetting location. The trap is switched off as
soon as the particle makes a first passage to the origin. Subsequently, the
particle resumes its free diffusion motion and the process keeps repeating. In
this set-up, the system attains a non-equilibrium steady state. We study the
relaxation to this steady state by analytically computing the position
distribution of the particle at all time and then analysing this distribution
using the spectral properties of the corresponding Fokker-Planck operator. As
seen for the instantaneous resetting problem, we observe a `cone spreading'
relaxation with travelling fronts such that there is an inner core region
around the resetting point that reaches the steady state, while the region
outside the core still grows ballistically with time. In addition to the
unusual relaxation phenomena, we compute the large deviation functions
associated to the corresponding probability density and find that the large
deviation functions describe a dynamical transition similar to what is seen
previously in case of instantaneous resetting. Notably, our method, based on
spectral properties, complements the existing renewal formalism and reveals the
intricate mathematical structure responsible for such relaxation phenomena. We
verify our analytical results against extensive numerical simulations. | cond-mat_stat-mech |
Criterion for phase separation in one-dimensional driven systems: A general criterion for the existence of phase separation in driven
one-dimensional systems is proposed. It is suggested that phase separation is
related to the size dependence of the steady-state currents of domains in the
system. A quantitative criterion for the existence of phase separation is
conjectured using a correspondence made between driven diffusive models and
zero-range processes. Several driven diffusive models are discussed in light of
the conjecture. | cond-mat_stat-mech |
Non-equilibrium steady state and induced currents of a
mesoscopically-glassy system: interplay of resistor-network theory and Sinai
physics: We introduce an explicit solution for the non-equilibrium steady state (NESS)
of a ring that is coupled to a thermal bath, and is driven by an external hot
source with log-wide distribution of couplings. Having time scales that stretch
over several decades is similar to glassy systems. Consequently there is a wide
range of driving intensities where the NESS is like that of a random walker in
a biased Brownian landscape. We investigate the resulting statistics of the
induced current $I$. For a single ring we discuss how $sign(I)$ fluctuates as
the intensity of the driving is increased, while for an ensemble of rings we
highlight the fingerprints of Sinai physics on the $abs(I)$ distribution. | cond-mat_stat-mech |
Interplay between writhe and knotting for swollen and compact polymers: The role of the topology and its relation with the geometry of biopolymers
under different physical conditions is a nontrivial and interesting problem.
Aiming at understanding this issue for a related simpler system, we use Monte
Carlo methods to investigate the interplay between writhe and knotting of ring
polymers in good and poor solvents. The model that we consider is interacting
self-avoiding polygons on the simple cubic lattice. For polygons with fixed
knot type we find a writhe distribution whose average depends on the knot type
but is insensitive to the length $N$ of the polygon and to solvent conditions.
This "topological contribution" to the writhe distribution has a value that is
consistent with that of ideal knots. The standard deviation of the writhe
increases approximately as $\sqrt{N}$ in both regimes and this constitutes a
geometrical contribution to the writhe. If the sum over all knot types is
considered, the scaling of the standard deviation changes, for compact
polygons, to $\sim N^{0.6}$. We argue that this difference between the two
regimes can be ascribed to the topological contribution to the writhe that, for
compact chains, overwhelms the geometrical one thanks to the presence of a
large population of complex knots at relatively small values of $N$. For
polygons with fixed writhe we find that the knot distribution depends on the
chosen writhe, with the occurrence of achiral knots being considerably
suppressed for large writhe. In general, the occurrence of a given knot thus
depends on a nontrivial interplay between writhe, chain length, and solvent
conditions. | cond-mat_stat-mech |
The Enskog equation for confined elastic hard spheres: A kinetic equation for a system of elastic hard spheres or disks confined by
a hard wall of arbitrary shape is derived. It is a generalization of the
modified Enskog equation in which the effects of the confinement are taken into
account and it is supposed to be valid up to moderate densities. From the
equation, balance equations for the hydrodynamic fields are derived,
identifying the collisional transfer contributions to the pressure tensor and
heat flux. A Lyapunov functional, $\mathcal{H}[f]$, is identified. For any
solution of the kinetic equation, $\mathcal{H}$ decays monotonically in time
until the system reaches the inhomogeneous equilibrium distribution, that is a
Maxwellian distribution with a the density field consistent with equilibrium
statistical mechanics. | cond-mat_stat-mech |
Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling
models: How robust are socioeconomic agent-based models with respect to the details
of the agents' decision rule? We tackle this question by considering an
occupation model in the spirit of the Sakoda-Schelling model, historically
introduced to shed light on segregation dynamics among human groups. For a
large class of utility functions and decision rules, we pinpoint the
nonequilibrium nature of the agent dynamics, while recovering the
equilibrium-like phase separation phenomenology. Within the mean field
approximation we show how the model can be mapped, to some extent, onto an
active matter field description (Active Model B). Finally, we consider
non-reciprocal interactions between two populations, and show how they can lead
to non-steady macroscopic behavior. We believe our approach provides a unifying
framework to further study geography-dependent agent-based models, notably
paving the way for joint consideration of population and price dynamics within
a field theoretic approach. | cond-mat_stat-mech |
Critical, crossover, and correction-to-scaling exponents for isotropic
Lifshitz points to order $\boldsymbol{(8-d)^2}$: A two-loop renormalization group analysis of the critical behaviour at an
isotropic Lifshitz point is presented. Using dimensional regularization and
minimal subtraction of poles, we obtain the expansions of the critical
exponents $\nu$ and $\eta$, the crossover exponent $\phi$, as well as the
(related) wave-vector exponent $\beta_q$, and the correction-to-scaling
exponent $\omega$ to second order in $\epsilon_8=8-d$. These are compared with
the authors' recent $\epsilon$-expansion results [{\it Phys. Rev. B} {\bf 62}
(2000) 12338; {\it Nucl. Phys. B} {\bf 612} (2001) 340] for the general case of
an $m$-axial Lifshitz point. It is shown that the expansions obtained here by a
direct calculation for the isotropic ($m=d$) Lifshitz point all follow from the
latter upon setting $m=8-\epsilon_8$. This is so despite recent claims to the
contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807]. | cond-mat_stat-mech |
Investigating Extreme Dependences: Concepts and Tools: We investigate the relative information content of six measures of dependence
between two random variables $X$ and $Y$ for large or extreme events for
several models of interest for financial time series. The six measures of
dependence are respectively the linear correlation $\rho^+_v$ and Spearman's
rho $\rho_s(v)$ conditioned on signed exceedance of one variable above the
threshold $v$, or on both variables ($\rho_u$), the linear correlation
$\rho^s_v$ conditioned on absolute value exceedance (or large volatility) of
one variable, the so-called asymptotic tail-dependence $\lambda$ and a
probability-weighted tail dependence coefficient ${\bar \lambda}$. The models
are the bivariate Gaussian distribution, the bivariate Student's distribution,
and the factor model for various distributions of the factor. We offer explicit
analytical formulas as well as numerical estimations for these six measures of
dependence in the limit where $v$ and $u$ go to infinity. This provides a
quantitative proof that conditioning on exceedance leads to conditional
correlation coefficients that may be very different from the unconditional
correlation and gives a straightforward mechanism for fluctuations or changes
of correlations, based on fluctuations of volatility or changes of trends.
Moreover, these various measures of dependence exhibit different and sometimes
opposite behaviors, suggesting that, somewhat similarly to risks whose adequate
characterization requires an extension beyond the restricted one-dimensional
measure in terms of the variance (volatility) to include all higher order
cumulants or more generally the knowledge of the full distribution,
tail-dependence has also a multidimensional character. | cond-mat_stat-mech |
Tensor Networks: Phase transition phenomena on hyperbolic and fractal
geometries: One of the challenging problems in the condensed matter physics is to
understand the quantum many-body systems, especially, their physical mechanisms
behind. Since there are only a few complete analytical solutions of these
systems, several numerical simulation methods have been proposed in recent
years. Amongst all of them, the Tensor Network algorithms have become
increasingly popular in recent years, especially for their adaptability to
simulate strongly correlated systems. The current work focuses on the
generalization of such Tensor-Network-based algorithms, which are sufficiently
robust to describe critical phenomena and phase transitions of multistate spin
Hamiltonians in the thermodynamic limit. We have chosen two algorithms: the
Corner Transfer Matrix Renormalization Group and the Higher-Order Tensor
Renormalization Group. This work, based on tensor-network analysis, opens doors
for the understanding of phase transition and entanglement of the interacting
systems on the non-Euclidean geometries. We focus on three main topics: A new
thermodynamic model of social influence, free energy is analyzed to classify
the phase transitions on an infinite set of the negatively curved geometries
where a relation between the free energy and the Gaussian radius of the
curvature is conjectured, a unique tensor-based algorithm is proposed to study
the phase transition on fractal structures. | cond-mat_stat-mech |
Competition Between Exchange and Anisotropy in a Pyrochlore Ferromagnet: The Ising-like spin ice model, with a macroscopically degenerate ground
state, has been shown to be approximated by several real materials. Here we
investigate a model related to spin ice, in which the Ising spins are replaced
by classical Heisenberg spins. These populate a cubic pyrochlore lattice and
are coupled to nearest neighbours by a ferromagnetic exchange term J and to the
local <1,1,1> axes by a single-ion anisotropy term D. The near neighbour spin
ice model corresponds to the case D/J infinite. For finite D/J we find that the
macroscopic degeneracy of spin ice is broken and the ground state is
magnetically ordered into a four-sublattice structure. The transition to this
state is first-order for D/J > 5 and second-order for D/J < 5 with the two
regions separated by a tricritical point. We investigate the magnetic phase
diagram with an applied field along [1,0,0] and show that it can be considered
analogous to that of a ferroelectric. | cond-mat_stat-mech |
Accessing power-law statistics under experimental constraints: Over the last decades, impressive progresses have been made in many
experimental domains, e.g. microscopic techniques such as single-particle
tracking, leading to plethoric amounts of data. In a large variety of systems,
from natural to socio-economic, the analysis of these experimental data
conducted us to conclude about the omnipresence of power-laws. For example, in
living systems, we are used to observing anomalous diffusion, e.g. in the
motion of proteins within the cell. However, estimating the power-law exponents
is challenging. Both technical constraints and experimental limitations affect
the statistics of observed data. Here, we investigate in detail the influence
of two essential constraints in the experiment, namely, the temporal-spatial
resolution and the time-window of the experiment. We study how the observed
distribution of an observable is modified by them and analytically derive the
expression of the power-law distribution for the observed distribution through
the scope of the experiment. We also apply our results on data from an
experimental study of the transport of mRNA-protein complexes along dendrites. | cond-mat_stat-mech |
Modelling High-frequency Economic Time Series: The minute-by-minute move of the Hang Seng Index (HSI) data over a four-year
period is analysed and shown to possess similar statistical features as those
of other markets. Based on a mathematical theorem [S. B. Pope and E. S. C.
Ching, Phys. Fluids A {\bf 5}, 1529 (1993)], we derive an analytic form for the
probability distribution function (PDF) of index moves from fitted functional
forms of certain conditional averages of the time series. Furthermore,
following a recent work by Stolovitzky and Ching, we show that the observed PDF
can be reproduced by a Langevin process with a move-dependent noise amplitude.
The form of the Langevin equation can be determined directly from the market
data. | cond-mat_stat-mech |
The three-state Potts antiferromagnet on plane quadrangulations: We study the antiferromagnetic 3-state Potts model on general (periodic)
plane quadrangulations $\Gamma$. Any quadrangulation can be built from a dual
pair $(G,G^*)$. Based on the duality properties of $G$, we propose a new
criterion to predict the phase diagram of this model. If $\Gamma$ is of
self-dual type (i.e., if $G$ is isomorphic to its dual $G^*$), the model has a
zero-temperature critical point with central charge $c=1$, and it is disordered
at all positive temperatures. If $\Gamma$ is of non-self-dual type (i.e., if
$G$ is not isomorphic to $G^*$), three ordered phases coexist at low
temperature, and the model is disordered at high temperature. In addition,
there is a finite-temperature critical point (separating these two phases)
which belongs to the universality class of the ferromagnetic 3-state Potts
model with central charge $c=4/5$. We have checked these conjectures by
studying four (resp. seven) quadrangulations of self-dual (resp. non-self-dual)
type, and using three complementary high-precision techniques: Monte-Carlo
simulations, transfer matrices, and critical polynomials. In all cases, we find
agreement with the conjecture. We have also found that the
Wang-Swendsen-Kotecky Monte Carlo algorithm does not have (resp. does have)
critical slowing down at the corresponding critical point on quadrangulations
of self-dual (resp. non-self-dual) type. | cond-mat_stat-mech |
Metropolis Monte Carlo algorithm based on the reparametrization
invariance: We introduce a modification of the well-known Metropolis importance sampling
algorithm by using a methodology inspired on the consideration of the
reparametrization invariance of the microcanonical ensemble. The most important
feature of the present proposal is the possibility of performing a suitable
description of microcanonical thermodynamic states during the first-order phase
transitions by using this local Monte Carlo algorithm. | cond-mat_stat-mech |
The Putative Liquid-Liquid Transition is a Liquid-Solid Transition in
Atomistic Models of Water, Part II: This paper extends our earlier studies of free energy functions of density
and crystalline order parameters for models of supercooled water, which allows
us to examine the possibility of two distinct metastable liquid phases [J.
Chem. Phys. 135, 134503 (2011) and arXiv:1107.0337v2]. Low-temperature
reversible free energy surfaces of several different atomistic models are
computed: mW water, TIP4P/2005 water, SW silicon and ST2 water, the last of
these comparing three different treatments of long-ranged forces. In each case,
we show that there is one stable or metastable liquid phase, and there is an
ice-like crystal phase. The time scales for crystallization in these systems
far exceed those of structural relaxation in the supercooled metastable liquid.
We show how this wide separation in time scales produces an illusion of a
low-temperature liquid-liquid transition. The phenomenon suggesting
metastability of two distinct liquid phases is actually coarsening of the
ordered ice-like phase, which we elucidate using both analytical theory and
computer simulation. For the latter, we describe robust methods for computing
reversible free energy surfaces, and we consider effects of electrostatic
boundary conditions. We show that sensible alterations of models and boundary
conditions produce no qualitative changes in low-temperature phase behaviors of
these systems, only marginal changes in equations of state. On the other hand,
we show that altering sampling time scales can produce large and qualitative
nonequilibrium effects. Recent reports of evidence of a liquid-liquid critical
point in computer simulations of supercooled water are considered in this
light. | cond-mat_stat-mech |
Understanding probability and irreversibility in the Mori-Zwanzig
projection operator formalism: Explaining the emergence of stochastic irreversible macroscopic dynamics from
time-reversible deterministic microscopic dynamics is one of the key problems
in philosophy of physics. The Mori-Zwanzig projection operator formalism, which
is one of the most important methods of modern nonequilibrium statistical
mechanics, allows for a systematic derivation of irreversible transport
equations from reversible microdynamics and thus provides a useful framework
for understanding this issue. However, discussions of the Mori-Zwanzig
formalism in philosophy of physics tend to focus on simple variants rather than
on the more sophisticated ones used in modern physical research. In this work,
I will close this gap by studying the problems of probability and
irreversibility using the example of Grabert's time-dependent projection
operator formalism. This allows to give a more solid mathematical foundation to
various concepts from the philosophical literature, in particular Wallace's
simple dynamical conjecture and Robertson's theory of autonomous macrodynamics.
Moreover, I will explain how the Mori-Zwanzig formalism allows to resolve the
tension between epistemic and ontic approaches to probability in statistical
mechanics. Finally, I argue that the debate which interventionists and
coarse-grainers should really be having is related not to the question why
there is equilibration at all, but why it has the quantitative form it is found
to have in experiments. | cond-mat_stat-mech |
Competition between Short-Ranged Attraction and Short-Ranged Repulsion
in Crowded Configurational Space; A Lattice Model Description: We describe a simple nearest-neighbor Ising model that is capable of
supporting a gas, liquid, crystal, in characteristic relationship to each
other. As the parameters of the model are varied one obtains characteristic
patterns of phase behavior reminiscent of continuum systems where the range of
the interaction is varied. The model also possesses dynamical arrest, and
although we have not studied it in detail, these 'transitions' appear to have a
reasonable relationship to the phases and their transitions. | cond-mat_stat-mech |
Statistical Properties of the Final State in One-dimensional Ballistic
Aggregation: We investigate the long time behaviour of the one-dimensional ballistic
aggregation model that represents a sticky gas of N particles with random
initial positions and velocities, moving deterministically, and forming
aggregates when they collide. We obtain a closed formula for the stationary
measure of the system which allows us to analyze some remarkable features of
the final `fan' state. In particular, we identify universal properties which
are independent of the initial position and velocity distributions of the
particles. We study cluster distributions and derive exact results for extreme
value statistics (because of correlations these distributions do not belong to
the Gumbel-Frechet-Weibull universality classes). We also derive the energy
distribution in the final state. This model generates dynamically many
different scales and can be viewed as one of the simplest exactly solvable
model of N-body dissipative dynamics. | cond-mat_stat-mech |
Network Mutual Information and Synchronization under Time
Transformations: We investigate the effect of general time transformations on the phase
synchronization (PS) phenomenon and the mutual information rate (MIR) between
pairs of nodes in dynamical networks. We demonstrate two important results
concerning the invariance of both PS and the MIR. Under time transformations PS
can neither be introduced nor destroyed and the MIR cannot be raised from zero.
On the other hand, for proper time transformations the timing between the
cycles of the coupled oscillators can be largely improved. Finally, we discuss
the relevance of our findings for communication in dynamical networks. | cond-mat_stat-mech |
A Random Force is a Force, of Course, of Coarse: Decomposing Complex
Enzyme Kinetics with Surrogate Models: The temporal autocorrelation (AC) function associated with monitoring order
parameters characterizing conformational fluctuations of an enzyme is analyzed
using a collection of surrogate models. The surrogates considered are
phenomenological stochastic differential equation (SDE) models. It is
demonstrated how an ensemble of such surrogate models, each surrogate being
calibrated from a single trajectory, indirectly contains information about
unresolved conformational degrees of freedom. This ensemble can be used to
construct complex temporal ACs associated with a "non-Markovian" process. The
ensemble of surrogates approach allows researchers to consider models more
flexible than a mixture of exponentials to describe relaxation times and at the
same time gain physical information about the system. The relevance of this
type of analysis to matching single-molecule experiments to computer
simulations and how more complex stochastic processes can emerge from a mixture
of simpler processes is also discussed. The ideas are illustrated on a toy SDE
model and on molecular dynamics simulations of the enzyme dihydrofolate
reductase. | cond-mat_stat-mech |
Thermodynamics of the Noninteracting Bose Gas in a Two-Dimensional Box: Bose-Einstein condensation (BEC) of a noninteracting Bose gas of N particles
in a two-dimensional box with Dirichlet boundary conditions is studied.
Confirming previous work, we find that BEC occurs at finite N at low
temperatures T without the occurrence of a phase transition. The
conventionally-defined transition temperature TE for an infinite 3D system is
shown to correspond in a 2D system with finite N to a crossover temperature
between a slow and rapid increase in the fractional boson occupation N0/N of
the ground state with decreasing T. We further show that TE ~ 1/log(N) at fixed
area per boson, so in the thermodynamic limit there is no significant BEC in 2D
at finite T. Thus, paradoxically, BEC only occurs in 2D at finite N with no
phase transition associated with it. Calculations of thermodynamic properties
versus T and area A are presented, including Helmholtz free energy, entropy S ,
pressure p, ratio of p to the energy density U/A, heat capacity at constant
volume (area) CV and at constant pressure Cp, isothermal compressibility
kappa_T and thermal expansion coefficient alpha_p, obtained using both the
grand canonical ensemble (GCE) and canonical ensemble (CE) formalisms. The GCE
formalism gives acceptable predictions for S, p, p/(U/A), kappa_T and alpha_p
at large N, T and A, but fails for smaller values of these three parameters for
which BEC becomes significant, whereas the CE formalism gives accurate results
for all thermodynamic properties of finite systems even at low T and/or A where
BEC occurs. | cond-mat_stat-mech |
Finite size spectrum of the staggered six-vertex model with
$U_q(\mathfrak{sl}(2))$-invariant boundary conditions: The finite size spectrum of the critical $\mathbb{Z}_2$-staggered spin-$1/2$
XXZ model with quantum group invariant boundary conditions is studied. For a
particular (self-dual) choice of the staggering the spectrum of conformal
weights of this model has been recently been shown to have a continuous
component, similar as in the model with periodic boundary conditions whose
continuum limit has been found to be described in terms of the non-compact
$SU(2,\mathbb{R})/U(1)$ Euclidean black hole conformal field theory (CFT). Here
we show that the same is true for a range of the staggering parameter. In
addition we find that levels from the discrete part of the spectrum of this CFT
emerge as the anisotropy is varied. The finite size amplitudes of both the
continuous and the discrete levels are related to the corresponding eigenvalues
of a quasi-momentum operator which commutes with the Hamiltonian and the
transfer matrix of the model. | cond-mat_stat-mech |
Manifestation of Random First Order Transition theory in Wigner glasses: We use Brownian dynamics simulations of a binary mixture of highly charged
spherical colloidal particles to illustrate many of the implications of the
Random First Order Transition (RFOT) theory (PRA 40 1045 (1989)), which is the
only theory that provides a unified description of both the statics and
dynamics of the liquid to glass transition. In accord with the RFOT, we find
that as the volume fraction of the colloidal particles \f, the natural variable
that controls glass formation in colloidal systems, approaches \f_A there is an
effective ergodic to non-ergodic dynamical transition, which is signalled by a
dramatic slowing down of diffusion. In addition, using the energy metric we
show that the system becomes non-ergodic as \f_A is approached. The time t^*,
at which the four-point dynamical susceptibility achieves a maximum, also
diverges near \f_A. Remarkably, three independent measures(translational
diffusion coefficients, ergodic diffusion coefficients,as well t^*) all signal
that at \f_A=0.1 ergodicity is effectively broken. The translation diffusion
constant, the ergodic diffusion constant, and (t^*)^-1 all vanish as
(\f_A-\f)^g with both \f_A and g being the roughly the same for all three
quantities. Below \f_A transport involves crossing suitable free energy
barriers. In this regime, the density-density correlation function decays as a
stretched exponential exp(-t/tau_a)^b with b=0.45. The \f-dependence of the
relaxation time \tau_a is well fit using the VFT law with the ideal glass
transition occurring at \f_K=0.47. By using an approximate measure of the local
entropy (s_3) we show that below \f_A the law of large numbers, which states
that the distribution of s_3 for a large subsample should be identical to the
whole sample, is not obeyed. The comprehensive analyses provided here for
Wigner glass forming charged colloidal suspensions fully validate the concepts
of the RFOT. | cond-mat_stat-mech |
How a local active force modifies the structural properties of polymers: We study the dynamics of a polymer, described as a variant of a Rouse chain,
driven by an active terminal monomer (head). The local active force induces a
transition from a globule-like to an elongated state, as revealed by the study
of the end-to-end distance, whose variance is analytically predicted under
suitable approximations. The change in the relaxation times of the Rouse-modes
produced by the local self-propulsion is consistent with the transition from
globule to elongated conformations. Moreover also the bond-bond spatial
correlation for the chain head results to be affected and a gradient of
over-stretched bonds along the chain is observed. We compare our numerical
results both with the phenomenological stiff-polymer theory and several
analytical predictions in the Rouse-chain approximation. | cond-mat_stat-mech |
On the Surface Tensions of Binary Mixtures: For binary mixtures with fixed concentrations of the species, various
relationships between the surface tensions and the concentrations are briefly
reviewed. | cond-mat_stat-mech |
Phase transition in a one-dimensional Ising ferromagnet at
zero-temperature under Glauber dynamics with a synchronous updating mode: In the past decade low-temperature Glauber dynamics for the one-dimensional
Ising system has been several times observed experimentally and occurred to be
one of the most important theoretical approaches in a field of molecular
nanomagnets. On the other hand, it has been shown recently that Glauber
dynamics with the Metropolis flipping probability for the zero-temperature
Ising ferromagnet under synchronous updating can lead surprisingly to the
antiferromagnetic steady state. In this paper the generalized class of Glauber
dynamics at zero-temperature will be considered and the relaxation into the
ground state, after a quench from high temperature, will be investigated. Using
Monte Carlo simulations and a mean field approach, discontinuous phase
transition between ferromagnetic and antiferromagnetic phases for a
one-dimensional ferromagnet will be shown. | cond-mat_stat-mech |
The non-equilibrium phase transition of the pair-contact process with
diffusion: The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles
is a simple branching-annihilation processes which exhibits a phase transition
from an active into an absorbing phase with an unusual type of critical
behaviour which had not been seen before. Although the model has attracted
considerable interest during the past few years it is not yet clear how its
critical behaviour can be characterized and to what extent the diffusive
pair-contact process represents an independent universality class. Recent
research is reviewed and some standing open questions are outlined. | cond-mat_stat-mech |
Universal microstructure and mechanical stability of jammed packings: Jammed packings' mechanical properties depend sensitively on their detailed
local structure. Here we provide a complete characterization of the pair
correlation close to contact and of the force distribution of jammed
frictionless spheres. In particular we discover a set of new scaling relations
that connect the behavior of particles bearing small forces and those bearing
no force but that are almost in contact. By performing systematic
investigations for spatial dimensions d=3-10, in a wide density range and using
different preparation protocols, we show that these scalings are indeed
universal. We therefore establish clear milestones for the emergence of a
complete microscopic theory of jamming. This description is also crucial for
high-precision force experiments in granular systems. | cond-mat_stat-mech |
Response to a small external force and fluctuations of a passive
particle in a one-dimensional diffusive environment: We investigate the long time behavior of a passive particle evolving in a
one-dimensional diffusive random environment, with diffusion constant $D$. We
consider two cases: (a) The particle is pulled forward by a small external
constant force, and (b) there is no systematic bias. Theoretical arguments and
numerical simulations provide evidence that the particle is eventually trapped
by the environment. This is diagnosed in two ways: The asymptotic speed of the
particle scales quadratically with the external force as it goes to zero, and
the fluctuations scale diffusively in the unbiased environment, up to possible
logarithmic corrections in both cases. Moreover, in the large $D$ limit
(homogenized regime), we find an important transient region giving rise to
other, finite-size scalings, and we describe the cross-over to the true
asymptotic behavior. | cond-mat_stat-mech |
Topological footprints of the 1D Kitaev chain with long range
superconducting pairings at a finite temperature: We study the 1D Kitaev chain with long range superconductive pairing terms at
a finite temperature where the system is prepared in a mixed state in
equilibrium with a heat reservoir maintained at a constant temperature $T$. In
order to probe the footprint of the ground state topological behavior of the
model at finite temperature, we look at two global quantities extracted out of
two geometrical constructions: the Uhlmann and the interferometric phase.
Interestingly, when the long-range effect dominates, the Uhlmann phase approach
fails to reproduce the topological aspects of the model in the pure state
limit; on the other hand, the interferometric phase, though has a proper pure
state reduction, shows a behaviour independent of the ambient temperature. | cond-mat_stat-mech |
Field-induced dynamics in the quantum Brownian oscillator: An exact
treatment: We consider a quantum linear oscillator coupled to a bath in equilibrium at
an arbitrary temperature and then exposed to an external field arbitrary in
form and strength. We then derive the reduced density operator in closed form
of the coupled oscillator in a non-equilibrium state at an arbitrary time. | cond-mat_stat-mech |
Localization threshold of Instantaneous Normal Modes from level-spacing
statistics: We study the statistics of level-spacing of Instantaneous Normal Modes in a
supercooled liquid. A detailed analysis allows to determine the mobility edge
separating extended and localized modes in the negative tail of the density of
states. We find that at temperature below the mode coupling temperature only a
very small fraction of negative eigenmodes are localized. | cond-mat_stat-mech |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.