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The influence of statistical properties of Fourier coefficients on
random surfaces: Many examples of natural systems can be described by random Gaussian
surfaces. Much can be learned by analyzing the Fourier expansion of the
surfaces, from which it is possible to determine the corresponding Hurst
exponent and consequently establish the presence of scale invariance. We show
that this symmetry is not affected by the distribution of the modulus of the
Fourier coefficients. Furthermore, we investigate the role of the Fourier
phases of random surfaces. In particular, we show how the surface is affected
by a non-uniform distribution of phases. | cond-mat_stat-mech |
Gaussian fluctuations in an ideal bose-gas -- a simple model: Based on the canonical ensemble, we suggested the simple scheme for taking
into account Gaussian fluctuations in a finite system of ideal boson gas.
Within framework of scheme we investigated the influence of fluctuations on the
particle distribution in Bose -gas for two cases - with taking into account the
number of particles in the ground state and without this assumption. The
temperature and fluctuation parameter dependences of the modified Bose-
Einstein distribution have been determined. Also the dependence of the
condensation temperature on the fluctuation distribution parameter has been
obtained. | cond-mat_stat-mech |
Pushing the limits of EPD zeros method: The use of partition function zeros in the study of phase transition is
growing in the last decade mainly due to improved numerical methods as well as
novel formulations and analysis. In this paper the impact of different
parameters choice for the energy probability distribution (EPD) zeros recently
introduced by Costa et al is explored in search for optimal values. Our results
indicate that the EPD method is very robust against parameter variations and
only small deviations on estimated critical temperatures are found even for
large variation of parameters, allowing to obtain accurate results with low
computational cost. A proposal to circumvent potential convergence issues of
the original algorithm is presented and validated for the case where it occurs. | cond-mat_stat-mech |
Intermolecular effects in the center-of-mass dynamics of unentangled
polymer fluids: We investigate the anomalous dynamics of unentangled polymer melts. The
proposed equation of motion formally relates the anomalous center-of-mass
diffusion, as observed in computer simulations and experiments, to the nature
of the effective intermolecular mean-force potential. An analytical
Gaussian-core form of the potential between the centers of mass of two polymers
is derived, which agrees with computer simulations and allows the analytical
solution of the equation of motion. The calculated center-of-mass dynamics is
characterized by an initial subdiffusive regime that persists for the spatial
range of the intermolecular mean-force potential, and for time intervals
shorter than the first intramolecular relaxation time, in agreement with
experiments and computer simulations of unentangled polymer melt dynamics. | cond-mat_stat-mech |
Large deviations and conditioning for chaotic non-invertible
deterministic maps: analysis via the forward deterministic dynamics and the
backward stochastic dynamics: The large deviations properties of trajectory observables for chaotic
non-invertible deterministic maps as studied recently by N. R. Smith, Phys.
Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C.
Perez-Espigares, arXiv:2304.13754 are revisited in order to analyze in detail
the similarities and the differences with the case of stochastic Markov chains.
To be concrete, we focus on the simplest example displaying the two essential
properties of local-stretching and global-folding, namely the doubling map $
x_{t+1} = 2 x_t [\text{mod} 1] $ on the real-space interval $x \in [0,1[$ that
can be also analyzed via the decomposition $x= \sum_{l=1}^{+\infty}
\frac{\sigma_l}{2^l} $ into binary coefficients $\sigma_l=0,1$. The large
deviations properties of trajectory observables can be studied either via
deformations of the forward deterministic dynamics or via deformations of the
backward stochastic dynamics. Our main conclusions concerning the construction
of the corresponding Doob canonical conditioned processes are: (i) non-trivial
conditioned dynamics can be constructed only in the backward stochastic
perspective where the reweighting of existing transitions is possible, and not
in the forward deterministic perspective ; (ii) the corresponding conditioned
steady state is not smooth on the real-space interval $x \in [0,1[$ and can be
better characterized in the binary space $\sigma_{l=1,2,..,+\infty}$. As a
consequence, the backward stochastic dynamics in the binary space is also the
most appropriate framework to write the explicit large deviations at level 2
for the probability of the empirical density of long backward trajectories. | cond-mat_stat-mech |
Renormalization-group study of the many-body localization transition in
one dimension: Using a new approximate strong-randomness renormalization group (RG), we
study the many-body localized (MBL) phase and phase transition in
one-dimensional quantum systems with short-range interactions and quenched
disorder. Our RG is built on those of Zhang $\textit{et al.}$ [1] and
Goremykina $\textit{et al.}$ [2], which are based on thermal and insulating
blocks. Our main addition is to characterize each insulating block with two
lengths: a physical length, and an internal decay length $\zeta$ for its
effective interactions. In this approach, the MBL phase is governed by a RG
fixed line that is parametrized by a global decay length $\tilde{\zeta}$, and
the rare large thermal inclusions within the MBL phase have a fractal geometry.
As the phase transition is approached from within the MBL phase,
$\tilde{\zeta}$ approaches the finite critical value corresponding to the
avalanche instability, and the fractal dimension of large thermal inclusions
approaches zero. Our analysis is consistent with a Kosterlitz-Thouless-like RG
flow, with no intermediate critical MBL phase. | cond-mat_stat-mech |
Statics and dynamics of the ten-state nearest-neighbor Potts glass on
the simple-cubic lattice: We present the results of Monte Carlo simulations of two different Potts
glass models with short range random interactions. In the first model a \pm
J-distribution of the bonds is chosen, in the second model a Gaussian
distribution. In both cases the first two moments of the distribution are
chosen to be J_0=-1, Delta J=+1, so that no ferromagnetic ordering of the Potts
spins can occur. We find that for all temperatures investigated the spin glass
susceptibility remains finite, the spin glass order parameter remains zero, and
that the specific heat has only a smooth Schottky-like peak. These results can
be understood quantitatively by considering small but independent clusters of
spins. Hence we have evidence that there is no static phase transition at any
nonzero temperature. Consistent with these findings, only very minor size
effects are observed, which implies that all correlation lengths of the models
remain very short. We also compute for both models the time auto-correlation
function C(t) of the Potts spins. While in the Gaussian model C(t) shows a
smooth uniform decay, the correlator for the \pm J model has several distinct
steps. These steps correspond to the breaking of bonds in small clusters of
ferromagnetically coupled spins (dimers, trimers, etc.). The relaxation times
follow simple Arrhenius laws, with activation energies that are readily
interpreted within the cluster picture, giving evidence that the system does
not have a dynamic transition at a finite temperature. Hence we find that for
the present models all the transitions known for the mean-field version of the
model are completely wiped out. Finally we also determine the time
auto-correlation functions of individual spins, and show that the system is
dynamically very heterogeneous. | cond-mat_stat-mech |
An Efficient Monte-Carlo Method for Calculating Free-Energy in
Long-Range Interacting Systems: We present an efficient Monte-Carlo method for long-range interacting systems
to calculate free energy as a function of an order parameter. In this method, a
variant of the Wang-Landau method regarding the order parameter is combined
with the stochastic cutoff method, which has recently been developed for
long-range interacting systems. This method enables us to calculate free energy
in long-range interacting systems with reasonable computational time despite
the fact that no approximation is involved. This method is applied to a
three-dimensional magnetic dipolar system to measure free energy as a function
of magnetization. By using the present method, we can calculate free energy for
a large system size of $16^3$ spins despite the presence of long-range magnetic
dipolar interactions. We also discuss the merits and demerits of the present
method in comparison with the conventional Wang-Landau method in which free
energy is calculated from the joint density of states of energy and order
parameter. | cond-mat_stat-mech |
Dynamical Rare event simulation techniques for equilibrium and
non-equilibrium systems: I give an overview of rare event simulation techniques to generate dynamical
pathways across high free energy barriers. The methods on which I will
concentrate are the reactive flux approach, transition path sampling,
(replica-exchange) transition interface sampling, partial path
sampling/milestoning, and forward flux sampling. These methods have in common
that they aim to simulate true molecular dynamics trajectories at a much faster
rate than naive brute force molecular dynamics. The advantages and
disadvantages of these methods are discussed and compared for a simple
one-dimensional test system. These numerical results reveal some important
pitfalls of the present non-equilibrium methods that have no easy solution and
show that caution is necessary when interpreting their results. | cond-mat_stat-mech |
Bose-Einstein condensation under external conditions: We discuss the phenomenon of Bose-Einstein condensation under general
external conditions using connections between partition sums and the
heat-equation. Thermodynamical quantities like the critical temperature are
given in terms of the heat-kernel coefficients of the associated Schr\"odinger
equation. The general approach is applied to situations where the gas is
confined by arbitrary potentials or by boxes of arbitrary shape. | cond-mat_stat-mech |
Exact thermodynamics and phase diagram of integrable t-J model with
chiral interaction: We study the phase diagram and finite temperature properties of an integrable
generalization of the one-dimensional super-symmetric t-J model containing
interactions explicitly breaking parity-time reversal (PT) symmetries. To this
purpose, we apply the quantum transfer matrix method which results in a finite
set of non-linear integral equations. We obtain numerical solutions to these
equations leading to results for thermodynamic quantities as function of
temperature, magnetic field, particle density and staggering parameter.
Studying the maxima lines of entropy at low but non zero temperature reveals
the phase diagram of the model. There are ten different phases which we may
classify in terms of the qualitative behaviour of auxiliary functions, closely
related to the dressed energy functions. | cond-mat_stat-mech |
Three lectures on statistical mechanics: These lectures were prepared for the 2014 PCMI graduate summer school and
were designed to be a lightweight introduction to statistical mechanics for
mathematicians. The applications feature some of the themes of the summer
school: sphere packings and tilings. | cond-mat_stat-mech |
Application of a time-convolutionless stochastic Schrödinger equation
to energy transport and thermal relaxation: Quantum stochastic methods based on effective wave functions form a framework
for investigating the generally non-Markovian dynamics of a quantum-mechanical
system coupled to a bath. They promise to be computationally superior to the
master-equation approach, which is numerically expensive for large dimensions
of the Hilbert space. Here, we numerically investigate the suitability of a
known stochastic Schr\"odinger equation that is local in time to give a
description of thermal relaxation and energy transport. This stochastic
Schr\"odinger equation can be solved with a moderate numerical cost, indeed
comparable to that of a Markovian system, and reproduces the dynamics of a
system evolving according to a general non-Markovian master equation. After
verifying that it describes thermal relaxation correctly, we apply it for the
first time to the energy transport in a spin chain. We also discuss a portable
algorithm for the generation of the coloured noise associated with the
numerical solution of the non-Markovian dynamics. | cond-mat_stat-mech |
Behavior of pressure and viscosity at high densities for two-dimensional
hard and soft granular materials: The pressure and the viscosity in two-dimensional sheared granular assemblies
are investigated numerically. The behavior of both pressure and viscosity is
smoothly changing qualitatively when starting from a mono-disperse hard-disk
system without dissipation and moving towards a system of (i) poly-disperse,
(ii) soft particles with (iii) considerable dissipation.
In the rigid, elastic limit of mono-disperse systems, the viscosity is
approximately inverse proportional to the area fraction difference from
$\phi_{\eta} \simeq 0.7$, but the pressure is still finite at $\phi_{\eta}$. In
moderately soft, dissipative and poly-disperse systems, on the other hand, we
confirm the recent theoretical prediction that both scaled pressure (divided by
the kinetic temperature $T$) and scaled viscosity (divided by $\sqrt{T}$)
diverge at the same density, i.e., the jamming transition point $\phi_J >
\phi_\eta$, with the exponents -2 and -3, respectively. Furthermore, we observe
that the critical region of the jamming transition becomes invisible as the
restitution coefficient approaches unity, i.e. for vanishing dissipation.
In order to understand the conflict between these two different predictions
on the divergence of the pressure and the viscosity, the transition from soft
to hard particles is studied in detail and the dimensionless control parameters
are defined as ratios of various time-scales. We introduce a dimensionless
number, i.e. the ratio of dissipation rate and shear rate, that can identify
the crossover from the scaling of very hard, i.e. rigid disks to the scaling in
the soft, jamming regime. | cond-mat_stat-mech |
Stochastic dynamics of N correlated binary variables and non-extensive
statistical mechanics: The non-extensive statistical mechanics has been applied to describe a
variety of complex systems with inherent correlations and feedback loops. Here
we present a dynamical model based on previously proposed static model
exhibiting in the thermodynamic limit the extensivity of the Tsallis entropy
with q<1 as well as a q-Gaussian distribution. The dynamical model consists of
a one-dimensional ring of particles characterized by correlated binary random
variables, which are allowed to flip according to a simple random walk rule.
The proposed dynamical model provides an insight how a mesoscopic dynamics
characterized by the non-extensive statistical mechanics could emerge from a
microscopic description of the system. | cond-mat_stat-mech |
Effective Temperature in an Interacting, Externally Driven, Vertex
System: Theory and Experiment on Artificial Spin Ice: Frustrated arrays of interacting single-domain nanomagnets provide important
model systems for statistical mechanics, because they map closely onto
well-studied vertex models and are amenable to direct imaging and custom
engineering. Although these systems are manifestly athermal, we demonstrate
that the statistical properties of both hexagonal and square lattices can be
described by an effective temperature based on the magnetostatic energy of the
arrays. This temperature has predictive power for the moment configurations and
is intimately related to how the moments are driven by an oscillating external
field. | cond-mat_stat-mech |
Thermodynamics of the Coarse-Graining Master Equation: We study the coarse-graining approach to derive a generator for the evolution
of an open quantum system over a finite time interval. The approach does not
require a secular approximation but nevertheless generally leads to a
Lindblad-Gorini-Kossakowski-Sudarshan generator. By combining the formalism
with Full Counting Statistics, we can demonstrate a consistent thermodynamic
framework, once the switching work required for the coupling and decoupling
with the reservoir is included. Particularly, we can write the second law in
standard form, with the only difference that heat currents must be defined with
respect to the reservoir. We exemplify our findings with simple but pedagogical
examples. | cond-mat_stat-mech |
Monte Carlo study of an anisotropic Ising multilayer with
antiferromagnetic interlayer couplings: We present a Monte Carlo study of the magnetic properties of an Ising
multilayer ferrimagnet. The system consists of two kinds of non-equivalent
planes, one of which is site-diluted. All intralayer couplings are
ferromagnetic. The different kinds of planes are stacked alternately and the
interlayer couplings are antiferromagnetic. We perform the simulations using
the Wolff algorithm and employ multiple histogram reweighting and finite-size
scaling methods to analyze the data with special emphasis on the study of
compensation phenomena. Compensation and critical temperatures of the system
are obtained as functions of the Hamiltonian parameters and we present a
detailed discussion about the contribution of each parameter to the presence or
absence of the compensation effect. A comparison is presented between our
results and those reported in the literature for the same model using the pair
approximation. We also compare our results with those obtained through both the
pair approximation and Monte Carlo simulations for the bilayer system. | cond-mat_stat-mech |
Fluctuations of isolated and confined surface steps of monoatomic height: The temporal evolution of equilibrium fluctuations for surface steps of
monoatomic height is analyzed studying one-dimensional solid-on-solid models.
Using Monte Carlo simulations, fluctuations due to periphery-diffusion (PD) as
well as due to evaporation-condensation (EC) are considered, both for isolated
steps and steps confined by the presence of straight steps. For isolated steps,
the dependence of the characteristic power-laws, their exponents and
prefactors, on temperature, slope, and curvature is elucidated, with the main
emphasis on PD, taking into account finite-size effects. The entropic repulsion
due to a second straight step may lead, among others, to an interesting
transient power-law like growth of the fluctuations, for PD. Findings are
compared to results of previous Monte Carlo simulations and predictions based,
mostly, on scaling arguments and Langevin theory. | cond-mat_stat-mech |
Anomalous behavior of ideal Fermi gas below two dimensions: Normal behavior of the thermodynamic properties of a Fermi gas in $d>2$
dimensions, integer or not, means monotonically increasing or decreasing of its
specific heat, chemical potential or isothermal sound velocity, all as
functions of temperature. However, for $0<d<2$ dimensions these properties
develop a ``hump'' (or ``trough'') which increases (or deepens) as $d\to 0$.
Though not the phase transition signaled by the sharp features (``cusp'' or
``jump'') in those properties for the ideal Bose gas in $d>2$ (known as the
Bose-Einstein condensation), it is nevertheless an intriguing structural
anomaly which we exhibit in detail. | cond-mat_stat-mech |
Freezing and clustering transitions for penetrable spheres: We consider a system of spherical particles interacting by means of a pair
potential equal to a finite constant for interparticle distances smaller than
the sphere diameter and zero outside. The model may be a prototype for the
interaction between micelles in a solvent [C. Marquest and T. A. Witten, J.
Phys. France 50, 1267 (1989)]. The phase diagram of these penetrable spheres is
investigated using a combination of cell- and density functional theory for the
solid phase together with simulations for the fluid phase. The system displays
unusual phase behavior due to the fact that, in the solid, the optimal
configuration is achieved when certain fractions of lattice sites are occupied
by more than one particle, a property that we call `clustering'. We find that
freezing from the fluid is followed, by increasing density, by a cascade of
second-order, clustering transitions in the crystal. | cond-mat_stat-mech |
Quantum critical behavior of itinerant ferromagnets: We investigate the quantum phase transition of itinerant ferromagnets. It is
shown that correlation effects in the underlying itinerant electron system lead
to singularities in the order parameter field theory that result in an
effective long-range interaction between the spin fluctuations. This
interaction turns out to be generically {\em antiferromagnetic} for clean
systems. In disordered systems analogous correlation effects lead to even
stronger singularities. The resulting long-range interaction is, however,
generically ferromagnetic.
We discuss two possibilities for the ferromagnetic quantum phase transition.
In clean systems, the transition is generically of first order, as is
experimentally observed in MnSi. However, under certain conditions the
transition may be continuous with non-mean field critical behavior. In
disordered systems, one finds a very rich phase diagram showing first order and
continuous phase transitions and several multicritical points. | cond-mat_stat-mech |
Information Geometry of q-Gaussian Densities and Behaviors of Solutions
to Related Diffusion Equations: This paper presents new geometric aspects of the behaviors of solutions to
the porous medium equation (PME) and its associated equation. First we discuss
the Legendre structure with information geometry on the manifold of generalized
exponential densities. Next by considering such a structure in particular on
the q-Gaussian densities, we derive several physically and geometrically
interesting properties of the solutions. They include, for example,
characterization of the moment-conserving projection of a solution, evaluation
of evolutional velocities of the second moments and the convergence rate to the
manifold in terms of the geodesic curves, divergence and so on. | cond-mat_stat-mech |
Dynamics of Granular Stratification: Spontaneous stratification in granular mixtures has been recently reported by
H. A. Makse et al. [Nature 386, 379 (1997)]. Here we study experimentally the
dynamical processes leading to spontaneous stratification. Using a high-speed
video camera, we study a rapid flow regime where the rolling grains size
segregate during the avalanche. We characterize the dynamical process of
stratification by measuring all relevant quantities: the velocity of the
rolling grains, the velocity of the kink, the wavelength of the layers, the
rate of collision between rolling and static grains, and all the angles of
repose characterizing the mixture. The wavelength of the layers behaves
linearly with the thickness of the layer of rolling grains (i.e., with the flow
rate), in agreement with theoretical predictions. The velocity profile of the
grains in the rolling phase is a linear function of the position of the grains
along the moving layer. We also find that the speed of the upward-moving kink
has the same value as the mean speed of the downward-moving grains. We measure
the shape and size of the kink, as well as the profiles of the rolling and
static phases of grains, and find agreement with recent theoretical
predictions. | cond-mat_stat-mech |
Mapping of the unoccupied states and relevant bosonic modes via the time
dependent momentum distribution: The unoccupied states of complex materials are difficult to measure, yet play
a key role in determining their properties. We propose a technique that can
measure the unoccupied states, called time-resolved Compton scattering, which
measures the time-dependent momentum distribution (TDMD). Using a
non-equilibrium Keldysh formalism, we study the TDMD for electrons coupled to a
lattice in a pump-probe setup. We find a direct relation between temporal
oscillations in the TDMD and the dispersion of the underlying unoccupied
states, suggesting that both can be measured by time-resolved Compton
scattering. We demonstrate the experimental feasibility by applying the method
to a model of MgB$_2$ with realistic material parameters. | cond-mat_stat-mech |
Preparation and relaxation of very stable glassy states of a simulated
liquid: We prepare metastable glassy states in a model glass-former made of
Lennard-Jones particles by sampling biased ensembles of trajectories with low
dynamical activity. These trajectories form an inactive dynamical phase whose
`fast' vibrational degrees of freedom are maintained at thermal equilibrium by
contact with a heat bath, while the `slow' structural degrees of freedom are
located in deep valleys of the energy landscape. We examine the relaxation to
equilibrium and the vibrational properties of these metastable states. The
glassy states we prepare by our trajectory sampling method are very stable to
thermal fluctuations and also more mechanically rigid than low-temperature
equilibrated configurations. | cond-mat_stat-mech |
Third-harmonic exponent in three-dimensional N-vector models: We compute the crossover exponent associated with the spin-3 operator in
three-dimensional O(N) models. A six-loop field-theoretical calculation in the
fixed-dimension approach gives $\phi_3 = 0.601(10)$ for the experimentally
relevant case N=2 (XY model). The corresponding exponent $\beta_3 = 1.413(10)$
is compared with the experimental estimates obtained in materials undergoing a
normal-incommensurate structural transition and in liquid crystals at the
smectic-A--hexatic-B phase transition, finding good agreement. | cond-mat_stat-mech |
Milestoning estimators of dissipation in systems observed at a coarse
resolution: When ignorance is truly bliss: Many non-equilibrium, active processes are observed at a coarse-grained
level, where different microscopic configurations are projected onto the same
observable state. Such "lumped" observables display memory, and in many cases
the irreversible character of the underlying microscopic dynamics becomes
blurred, e.g., when the projection hides dissipative cycles. As a result, the
observations appear less irreversible, and it is very challenging to infer the
degree of broken time-reversal symmetry. Here we show, contrary to intuition,
that by ignoring parts of the already coarse-grained state space we may -- via
a process called milestoning -- improve entropy-production estimates.
Milestoning systematically renders observations "closer to underlying
microscopic dynamics" and thereby improves thermodynamic inference from lumped
data assuming a given range of memory. Moreover, whereas the correct general
physical definition of time-reversal in the presence of memory remains unknown,
we here show by means of systematic, physically relevant examples that at least
for semi-Markov processes of first and second order, waiting-time contributions
arising from adopting a naive Markovian definition of time-reversal generally
must be discarded. | cond-mat_stat-mech |
Universal threshold for the dynamical behavior of lattice systems with
long-range interactions: Dynamical properties of lattice systems with long-range pair interactions,
decaying like 1/r^{\alpha} with the distance r, are investigated, in particular
the time scales governing the relaxation to equilibrium. Upon varying the
interaction range \alpha, we find evidence for the existence of a threshold at
\alpha=d/2, dependent on the spatial dimension d, at which the relaxation
behavior changes qualitatively and the corresponding scaling exponents switch
to a different regime. Based on analytical as well as numerical observations in
systems of vastly differing nature, ranging from quantum to classical, from
ferromagnetic to antiferromagnetic, and including a variety of lattice
structures, we conjecture this threshold and some of its characteristic
properties to be universal. | cond-mat_stat-mech |
Spontaneous symmetry breaking and Nambu-Goldstone modes in dissipative
systems: We discuss spontaneous breaking of internal symmetry and its Nambu-Goldstone
(NG) modes in dissipative systems. We find that there exist two types of NG
modes in dissipative systems corresponding to type-A and type-B NG modes in
Hamiltonian systems. To demonstrate the symmetry breaking, we consider a $O(N)$
scalar model obeying a Fokker-Planck equation. We show that the type-A NG modes
in the dissipative system are diffusive modes, while they are propagating modes
in Hamiltonian systems. We point out that this difference is caused by the
existence of two types of Noether charges, $Q_R^\alpha$ and $Q_A^\alpha$:
$Q_R^\alpha$ are symmetry generators of Hamiltonian systems, which are not
conserved in dissipative systems. $Q_A^\alpha$ are symmetry generators of
dissipative systems described by the Fokker-Planck equation, which are
conserved. We find that the NG modes are propagating modes if $Q_R^\alpha$ are
conserved, while those are diffusive modes if they are not conserved. We also
consider a $SU(2)\times U(1)$ scalar model with a chemical potential to discuss
the type-B NG modes. We show that the type-B NG modes have a different
dispersion relation from those in the Hamiltonian systems. | cond-mat_stat-mech |
Comment on ``Solution of Classical Stochastic One-Dimensional Many-Body
Systems'': In a recent Letter, Bares and Mobilia proposed the method to find solutions
of the stochastic evolution operator $H=H_0 + {\gamma\over L} H_1$ with a
non-trivial quartic term $H_1$. They claim, ``Because of the conservation of
probability, an analog of the Wick theorem applies and all multipoint
correlation functions can be computed.'' Using the Wick theorem, they expressed
the density correlation functions as solutions of a closed set of
integro-differential equations.
In this Comment, however, we show that applicability of Wick theorem is
restricted to the case $\gamma = 0$ only. | cond-mat_stat-mech |
Random Walk over Basins of Attraction to Construct Ising Energy
Landscapes: An efficient algorithm is developed to construct disconnectivity graphs by a
random walk over basins of attraction. This algorithm can detect a large number
of local minima, find energy barriers between them, and estimate local thermal
averages over each basin of attraction. It is applied to the SK spin glass
Hamiltonian where existing methods have difficulties even for a moderate number
of spins. Finite-size results are used to make predictions in the thermodynamic
limit that match theoretical approximations and recent findings on the free
energy landscapes of SK spin glasses. | cond-mat_stat-mech |
Einstein relation and hydrodynamics of nonequilibrium mass transport
processes: We obtain hydrodynamic descriptions of a broad class of conserved-mass
transport processes on a ring. These processes are governed by chipping,
diffusion and coalescence of masses, where microscopic probability weights in
their nonequilibrium steady states, having nontrivial correlations, are not
known. In these processes, we analytically calculate two transport
coefficients, the bulk-diffusion coefficient and the conductivity. We,
remarkably, find that the two transport coefficients obey an equilibriumlike
Einstein relation, although the microscopic dynamics does not satisfy detailed
balance condition. Using macroscopic fluctuation theory, we also show that
probability of density fluctuations obtained from the hydrodynamic description
is in complete agreement with the same derived earlier in [Phys. Rev. E 93,
062135 (2016)] using an additivity property. | cond-mat_stat-mech |
Modelling quasicrystals at positive temperature: We consider a two-dimensional lattice model of equilibrium statistical
mechanics, using nearest neighbor interactions based on the matching conditions
for an aperiodic set of 16 Wang tiles. This model has uncountably many ground
state configurations, all of which are nonperiodic. The question addressed in
this paper is whether nonperiodicity persists at low but positive temperature.
We present arguments, mostly numerical, that this is indeed the case. In
particular, we define an appropriate order parameter, prove that it is
identically zero at high temperatures, and show by Monte Carlo simulation that
it is nonzero at low temperatures. | cond-mat_stat-mech |
Correlation Effects in Ultracold Two-Dimensional Bose Gases: We study various properties of an ultracold two-dimensional (2D) Bose gas
that are beyond a mean-field description. We first derive the effective
interaction for such a system as realized in current experiments, which
requires the use of an energy dependent $T$-matrix. Using this result, we then
solve the mean-field equation of state of the modified Popov theory, and
compare it with the usual Hartree-Fock theory. We show that even though the
former theory does not suffer from infrared divergences in both the normal and
superfluid phases, there is an unphysical density discontinuity close to the
Berezinskii-Kosterlitz-Thouless transition. We then improve upon the mean-field
description by using a renormalization group approach and show how the density
discontinuity is resolved. The flow equations in two dimensions, in particular,
of the symmetry-broken phase, already contain some unique features pertinent to
the 2D XY model, even though vortices have not been included explicitly. We
also compute various many-body correlators, and show that correlation effects
beyond the Hartree-Fock theory are important already in the normal phase as
criticality is approached. We finally extend our results to the inhomogeneous
case of a trapped Bose gas using the local-density approximation and show that
close to criticality, the renormalization group approach is required for the
accurate determination of the density profile. | cond-mat_stat-mech |
Nanowire reconstruction under external magnetic fields: We consider the different structures that a magnetic nanowire adsorbed on a
surface may adopt under the influence of external magnetic or electric fields.
First, we propose a theoretical framework based on an Ising-like extension of
the 1D Frenkel-Kontorova model, which is analysed in detail using the transfer
matrix formalism, determining a rich phase diagram displaying structural
reconstructions at finite fields and an antiferromagnetic-paramagnetic phase
transition of second order. Our conclusions are validated using ab initio
calculations with density functional theory, paving the way for the search of
actual materials where this complex phenomenon can be observed in the
laboratory. | cond-mat_stat-mech |
Quantum critical behaviors and decoherence of weakly coupled quantum
Ising models within an isolated global system: We discuss the quantum dynamics of an isolated composite system consisting of
weakly interacting many-body subsystems. We focus on one of the subsystems, S,
and study the dependence of its quantum correlations and decoherence rate on
the state of the weakly-coupled complementary part E, which represents the
environment. As a theoretical laboratory, we consider a composite system made
of two stacked quantum Ising chains, locally and homogeneously weakly coupled.
One of the chains is identified with the subsystem S under scrutiny, and the
other one with the environment E. We investigate the behavior of S at
equilibrium, when the global system is in its ground state, and under
out-of-equilibrium conditions, when the global system evolves unitarily after a
soft quench of the coupling between S and E. When S develops quantum critical
correlations in the weak-coupling regime, the associated scaling behavior
crucially depends on the quantum state of E whether it is characterized by
short-range correlations (analogous to those characterizing disordered phases
in closed systems), algebraically decaying correlations (typical of critical
systems), or long-range correlations (typical of magnetized ordered phases). In
particular, different scaling behaviors, depending on the state of E, are
observed for the decoherence of the subsystem S, as demonstrated by the
different power-law divergences of the decoherence susceptibility that
quantifies the sensitivity of the coherence to the interaction with E. | cond-mat_stat-mech |
Fluctuations and correlations in hexagonal optical patterns: We analyze the influence of noise in transverse hexagonal patterns in
nonlinear Kerr cavities. The near field fluctuations are determined by the
neutrally stable Goldstone modes associated to translational invariance and by
the weakly damped soft modes. However these modes do not contribute to the far
field intensity fluctuations which are dominated by damped perturbations with
the same wave vectors than the pattern. We find strong correlations between the
intensity fluctuations of any arbitrary pair of wave vectors of the pattern.
Correlation between pairs forming 120 degrees is larger than between pairs
forming 180 degrees, contrary to what a naive interpretation of emission in
terms of twin photons would suggest. | cond-mat_stat-mech |
Knot probabilities in equilateral random polygons: We consider the probability of knotting in equilateral random polygons in
Euclidean 3-dimensional space, which model, for instance, random polymers.
Results from an extensive Monte Carlo dataset of random polygons indicate a
universal scaling formula for the knotting probability with the number of
edges. This scaling formula involves an exponential function, independent of
knot type, with a power law factor that depends on the number of prime
components of the knot. The unknot, appearing as a composite knot with zero
components, scales with a small negative power law, contrasting with previous
studies that indicated a purely exponential scaling. The methodology
incorporates several improvements over previous investigations: our random
polygon data set is generated using a fast, unbiased algorithm, and knotting is
detected using an optimised set of knot invariants based on the Alexander
polynomial. | cond-mat_stat-mech |
The effect of disorder on the hierarchical modularity in complex systems: We consider a system hierarchically modular, if besides its hierarchical
structure it shows a sequence of scale separations from the point of view of
some functionality or property. Starting from regular, deterministic objects
like the Vicsek snowflake or the deterministic scale free network by Ravasz et
al. we first characterize the hierarchical modularity by the periodicity of
some properties on a logarithmic scale indicating separation of scales. Then we
introduce randomness by keeping the scale freeness and other important
characteristics of the objects and monitor the changes in the modularity. In
the presented examples sufficient amount of randomness destroys hierarchical
modularity. Our findings suggest that the experimentally observed hierarchical
modularity in systems with algebraically decaying clustering coefficients
indicates a limited level of randomness. | cond-mat_stat-mech |
Generalized Entropies and Statistical Mechanics: We consider the problem of defining free energy and other thermodynamic
functions when the entropy is given as a general function of the probablity
distribution, including that for non extensive forms. We find that the free
energy, which is central to the determination of all other quantities, can be
obtained uniquely numerically ebven when it is the root of a transcendental
equation. In particular we study the cases for Tsallis form and a new form
proposed by us recently. We compare the free energy, the internal energy and
the specific heat of a simple system two energy states for each of these forms. | cond-mat_stat-mech |
Minimal entropy production in the presence of anisotropic fluctuations: Anisotropy in temperature, chemical potential, or ion concentration, provides
the fuel that feeds dynamical processes that sustain life. At the same time,
anisotropy is a root cause of incurred losses manifested as entropy production.
In this work we consider a rudimentary model of an overdamped stochastic
thermodynamic system in an anisotropic temperature heat bath, and study minimum
entropy production when driving the system between thermodynamic states in
finite time. While entropy production in isotropic temperature environments can
be expressed in terms of the length (in the Wasserstein-2 metric) traversed by
the thermodynamic state of the system, anisotropy complicates substantially the
mechanism of entropy production since, besides dissipation, seepage of energy
between ambient anisotropic heat sources by way of the system dynamics is often
a major contributing factor. A key result of the paper is to show that in the
presence of anisotropy, minimization of entropy production can once again be
expressed via a modified Optimal Mass Transport (OMT) problem. However, in
contrast to the isotropic situation that leads to a classical OMT problem and a
Wasserstein length, entropy production may not be identically zero when the
thermodynamic state remains unchanged (unless one has control over
non-conservative forces); this is due to the fact that maintaining a
Non-Equilibrium Steady-State (NESS) incurs an intrinsic entropic cost that can
be traced back to a seepage of heat between heat baths. As alluded to, NESSs
represent hallmarks of life, since living matter by necessity operates far from
equilibrium. Therefore, the question studied herein, to characterize minimal
entropy production in anisotropic environments, appears of central importance
in biological processes and on how such processes may have evolved to optimize
for available usage of resources. | cond-mat_stat-mech |
Metastability for a stochastic dynamics with a parallel heat bath
updating rule: We consider the problem of metastability for a stochastic dynamics with a
parallel updating rule with single spin rates equal to those of the heat bath
for the Ising nearest neighbors interaction. We study the exit from the
metastable phase, we describe the typical exit path and evaluate the exit time.
We prove that the phenomenology of metastability is different from the one
observed in the case of the serial implementation of the heat bath dynamics. In
particular we prove that an intermediate chessboard phase appears during the
excursion from the minus metastable phase toward the plus stable phase. | cond-mat_stat-mech |
Exploring Conformational Landscapes Along Anharmonic Low-Frequency
Vibrations: We aim to automatize the identification of collective variables to simplify
and speed up enhanced sampling simulations of conformational dynamics in
biomolecules. We focus on anharmonic low-frequency vibrations that exhibit
fluctuations on timescales faster than conformational transitions but describe
a path of least resistance towards structural change. A key challenge is that
harmonic approximations are ill-suited to characterize these vibrations, which
are observed at far-infrared frequencies and are easily excited by thermal
collisions at room temperature.
Here, we approached this problem with a frequency-selective anharmonic
(FRESEAN) mode analysis that does not rely on harmonic approximations and
successfully isolates anharmonic low-frequency vibrations from short molecular
dynamics simulation trajectories. We applied FRESEAN mode analysis to
simulations of alanine dipeptide, a common test system for enhanced sampling
simulation protocols, and compare the performance of isolated low-frequency
vibrations to conventional user-defined collective variables (here backbone
dihedral angles) in enhanced sampling simulations.
The comparison shows that enhanced sampling along anharmonic low-frequency
vibrations not only reproduces known conformational dynamics but can even
further improve sampling of slow transitions compared to user-defined
collective variables. Notably, free energy surfaces spanned by low-frequency
anharmonic vibrational modes exhibit lower barriers associated with
conformational transitions relative to representations in backbone dihedral
space. We thus conclude that anharmonic low-frequency vibrations provide a
promising path for highly effective and fully automated enhanced sampling
simulations of conformational dynamics in biomolecules. | cond-mat_stat-mech |
Forward-Flux Sampling with Jumpy Order Parameters: Forward-flux sampling (FFS) is a path sampling technique that has gained
increased popularity in recent years, and has been used to compute rates of
rare event phenomena such as crystallization, condensation, hydrophobic
evaporation, DNA hybridization and protein folding. The popularity of FFS is
not only due to its ease of implementation, but also because it is not very
sensitive to the particular choice of an order parameter. The order parameter
utilized in conventional FFS, however, still needs to satisfy a stringent
smoothness criterion in order to assure sequential crossing of FFS milestones.
This condition is usually violated for order parameters utilized for describing
aggregation phenomena such as crystallization. Here, we present a generalized
FFS algorithm for which this smoothness criterion is no longer necessary, and
apply it to compute homogeneous crystal nucleation rates in several systems.
Our numerical tests reveal that conventional FFS can sometimes underestimate
the nucleation rate by several orders of magnitude. | cond-mat_stat-mech |
Extreme event statistics of daily rainfall: Dynamical systems approach: We analyse the probability densities of daily rainfall amounts at a variety
of locations on the Earth. The observed distributions of the amount of rainfall
fit well to a q-exponential distribution with exponent q close to q=1.3. We
discuss possible reasons for the emergence of this power law. On the contrary,
the waiting time distribution between rainy days is observed to follow a
near-exponential distribution. A careful investigation shows that a
q-exponential with q=1.05 yields actually the best fit of the data. A Poisson
process where the rate fluctuates slightly in a superstatistical way is
discussed as a possible model for this. We discuss the extreme value statistics
for extreme daily rainfall, which can potentially lead to flooding. This is
described by Frechet distributions as the corresponding distributions of the
amount of daily rainfall decay with a power law. On the other hand, looking at
extreme event statistics of waiting times between rainy days (leading to
droughts for very long dry periods) we obtain from the observed
near-exponential decay of waiting times an extreme event statistics close to
Gumbel distributions. We discuss superstatistical dynamical systems as simple
models in this context. | cond-mat_stat-mech |
On the typical properties of inverse problems in statistical mechanics: In this work we consider the problem of extracting a set of interaction
parameters from an high-dimensional dataset describing T independent
configurations of a complex system composed of N binary units. This problem is
formulated in the language of statistical mechanics as the problem of finding a
family of couplings compatible with a corresponding set of empirical
observables in the limit of large N. We focus on the typical properties of its
solutions and highlight the possible spurious features which are associated
with this regime (model condensation, degenerate representations of data,
criticality of the inferred model). We present a class of models (complete
models) for which the analytical solution of this inverse problem can be
obtained, allowing us to characterize in this context the notion of stability
and locality. We clarify the geometric interpretation of some of those aspects
by using results of differential geometry, which provides means to quantify
consistency, stability and criticality in the inverse problem. In order to
provide simple illustrative examples of these concepts we finally apply these
ideas to datasets describing two stochastic processes (simulated realizations
of a Hawkes point-process and a set of time-series describing financial
transactions in a real market). | cond-mat_stat-mech |
Counter-ion density profile around charged cylinders: the
strong-coupling needle limit: Charged rod-like polymers are not able to bind all their neutralizing
counter-ions: a fraction of them evaporates while the others are said to be
condensed. We study here counter-ion condensation and its ramifications, both
numerically by means of Monte Carlo simulations employing a previously
introduced powerful logarithmic sampling of radial coordinates, and
analytically, with special emphasis on the strong-coupling regime. We focus on
the thin rod, or needle limit, that is naturally reached under strong coulombic
couplings, where the typical inter-particle spacing $a'$ along the rod is much
larger than its radius R. This regime is complementary and opposite to the
simpler thick rod case where $a'\ll R$. We show that due account of counter-ion
evaporation, a universal phenomenon in the sense that it occurs in the same
clothing for both weakly and strongly coupled systems, allows to obtain
excellent agreement between the numerical simulations and the strong-coupling
calculations. | cond-mat_stat-mech |
Monte Carlo Results for Projected Self-Avoiding Polygons: A
Two-dimensional Model for Knotted Polymers: We introduce a two-dimensional lattice model for the description of knotted
polymer rings. A polymer configuration is modeled by a closed polygon drawn on
the square diagonal lattice, with possible crossings describing pairs of
strands of polymer passing on top of each other. Each polygon configuration can
be viewed as the two- dimensional projection of a particular knot. We study
numerically the statistics of large polygons with a fixed knot type, using a
generalization of the BFACF algorithm for self-avoiding walks. This new
algorithm incorporates both the displacement of crossings and the three types
of Reidemeister transformations preserving the knot topology. Its ergodicity
within a fixed knot type is not proven here rigorously but strong arguments in
favor of this ergodicity are given together with a tentative sketch of proof.
Assuming this ergodicity, we obtain numerically the following results for the
statistics of knotted polygons: In the limit of a low crossing fugacity, we
find a localization along the polygon of all the primary factors forming the
knot. Increasing the crossing fugacity gives rise to a transition from a
self-avoiding walk to a branched polymer behavior. | cond-mat_stat-mech |
Construction of the factorized steady state distribution in models of
mass transport: For a class of one-dimensional mass transport models we present a simple and
direct test on the chipping functions, which define the probabilities for mass
to be transferred to neighbouring sites, to determine whether the stationary
distribution is factorized. In cases where the answer is affirmative, we
provide an explicit method for constructing the single-site weight function. As
an illustration of the power of this approach, previously known results on the
Zero-range process and Asymmetric random average process are recovered in a few
lines. We also construct new models, namely a generalized Zero-range process
and a binomial chipping model, which have factorized steady states. | cond-mat_stat-mech |
Large Deviations of Convex Hulls of the "True" Self-Avoiding Random Walk: We study the distribution of the area and perimeter of the convex hull of the
"true" self-avoiding random walk in a plane. Using a Markov chain Monte Carlo
sampling method, we obtain the distributions also in their far tails, down to
probabilities like $10^{-800}$. This enables us to test previous conjectures
regarding the scaling of the distribution and the large-deviation rate function
$\Phi$. In previous studies, e.g., for standard random walks, the whole
distribution was governed by the Flory exponent $\nu$. We confirm this in the
present study by considering expected logarithmic corrections. On the other
hand, the behavior of the rate function deviates from the expected form. For
this exception we give a qualitative reasoning. | cond-mat_stat-mech |
Boltzmann's entropy during free expansion of an interacting ideal gas: In this work we study the evolution of Boltzmann's entropy in the context of
free expansion of a one dimensional interacting gas inside a box. Boltzmann's
entropy is defined for single microstates and is given by the phase-space
volume occupied by microstates with the same value of macrovariables which are
coarse-grained physical observables. We demonstrate the idea of typicality in
the growth of the Boltzmann's entropy for two choices of macro-variables -- the
single particle phase space distribution and the hydrodynamic fields. Due to
the presence of interaction, the growth curves for both these entropies are
observed to converge to a monotonically increasing limiting curve, on taking
the appropriate order of limits, of large system size and small coarse graining
scale. Moreover, we observe that the limiting growth curves for the two choices
of entropies are identical as implied by local thermal equilibrium. We also
discuss issues related to finite size and finite coarse gaining scale which
lead interesting features such as oscillations in the entropy growth curve. We
also discuss shocks observed in the hydrodynamic fields. | cond-mat_stat-mech |
Levy Flights in Inhomogeneous Media: We investigate the impact of external periodic potentials on superdiffusive
random walks known as Levy flights and show that even strongly superdiffusive
transport is substantially affected by the external field. Unlike ordinary
random walks, Levy flights are surprisingly sensitive to the shape of the
potential while their asymptotic behavior ceases to depend on the Levy index
$\mu $. Our analysis is based on a novel generalization of the Fokker-Planck
equation suitable for systems in thermal equilibrium. Thus, the results
presented are applicable to the large class of situations in which
superdiffusion is caused by topological complexity, such as diffusion on folded
polymers and scale-free networks. | cond-mat_stat-mech |
Generalized Theory of Landau Damping: Collisionless damping of electrical waves in plasma is investigated in the
frame of the classical formulation of the problem. The new principle of
regularization of the singular integral is used. The exact solution of the
corresponding dispersion equation is obtained. The results of calculations lead
to existence of discrete spectrum of frequencies and discrete spectrum of
dispersion curves. Analytical results are in good coincidence with results of
direct mathematical experiments. Key words: Foundations of the theory of
transport processes and statistical physics; Boltzmann physical kinetics;
damping of plasma waves, linear theory of wave`s propagation PACS: 67.55.Fa,
67.55.Hc | cond-mat_stat-mech |
An axiomatic characterization of a two-parameter extended relative
entropy: The uniqueness theorem for a two-parameter extended relative entropy is
proven. This result extends our previous one, the uniqueness theorem for a
one-parameter extended relative entropy, to a two-parameter case. In addition,
the properties of a two-parameter extended relative entropy are studied. | cond-mat_stat-mech |
Dominance of extreme statistics in a prototype many-body Brownian
ratchet: Many forms of cell motility rely on Brownian ratchet mechanisms that involve
multiple stochastic processes. We present a computational and theoretical study
of the nonequilibrium statistical dynamics of such a many-body ratchet, in the
specific form of a growing polymer gel that pushes a diffusing obstacle. We
find that oft-neglected correlations among constituent filaments impact
steady-state kinetics and significantly deplete the gel's density within
molecular distances of its leading edge. These behaviors are captured
quantitatively by a self-consistent theory for extreme fluctuations in
filaments' spatial distribution. | cond-mat_stat-mech |
Nematic - Isotropic Transition in Porous Media - a Monte Carlo Study: We propose a lattice model to simulate the influence of porous medium on the
Nematic - Isotropic transition of liquid crystal confined to the pores. The
effects of pore size and pore connectivity are modelled through a disorder
parameter. Monte Carlo calculations based on the model leads to results that
compare well with experiments. | cond-mat_stat-mech |
A Worm Algorithm for Two-Dimensional Spin Glasses: A worm algorithm is proposed for the two-dimensional spin glasses. The method
is based on a low-temperature expansion of the partition function. The
low-temperature configurations of the spin glass on square lattice can be
viewed as strings connecting pairs of frustrated plaquettes. The worm algorithm
directly manipulates these strings. It is shown that the worm algorithm is as
efficient as any other types of cluster or replica-exchange algorithms. The
worm algorithm is even more efficient if free boundary conditions are used. We
obtain accurate low-temperature specific heat data consistent with a form c =
T^{-2} exp(-2J/(k_BT)), where T is temperature and J is coupling constant, for
the +/-J two-dimensional spin glass. | cond-mat_stat-mech |
Variation along liquid isomorphs of the driving force for
crystallization: We investigate the variation of the driving force for crystallization of a
supercooled liquid along isomorphs, curves along which structure and dynamics
are invariant. The variation is weak, and can be predicted accurately for the
Lennard-Jones fluid using a recently developed formalism and data at a
reference temperature. More general analysis allows interpretation of
experimental data for molecular liquids such as dimethyl phthalate and
indomethacin, and suggests that the isomorph scaling exponent $\gamma$ in these
cases is an increasing function of density, although this cannot be seen in
measurements of viscosity or relaxation time. | cond-mat_stat-mech |
Comment on ``Deterministic equations of motion and phase ordering
dynamics'': Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase
ordering dynamics in the microcanonical $\phi^4$ model displays unusual scaling
laws. We show here, performing more careful numerical investigations, that
Zheng only observed transient dynamics mostly due to the corrections to scaling
introduced by lattice effects, and that Ising-like (model A) phase ordering
actually takes place at late times. Moreover, we argue that energy conservation
manifests itself in different corrections to scaling. | cond-mat_stat-mech |
Anisotropies of the Hamiltonian and the Wave Function: Inversion
Phenomena in Quantum Spin Chains: We investigate the inversion phenomenon between the XXZ anisotropies of the
Hamiltonian and the wave function in quantum spin chains, mainly focusing on
the S=1/2 trimerized XXZ model with the next-nearest-neighbor interactions. We
have obtained the ground-state phase diagram by use of the degenerate
perturbation theory and the level spectroscopy analysis of the numerical data
calculated by the Lanczos method. In some parameter regions, the spin-fluid is
realized for the Ising-like anisotropy, and the Neel state for the XY-like
anisotropy, against the ordinary situation. | cond-mat_stat-mech |
Instanton Approach to Large $N$ Harish-Chandra-Itzykson-Zuber Integrals: We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber
integrals. We provide, using Dyson's Brownian motion and the method of
instantons, an alternative, transparent derivation of the Matytsin formalism
for the unitary case. Our method is easily generalized to the orthogonal and
symplectic ensembles. We obtain an explicit solution of Matytsin's equations in
the case of Wigner matrices, as well as a general expansion method in the
dilute limit, when the spectrum of eigenvalues spreads over very wide regions. | cond-mat_stat-mech |
Resonant diffusion on solid surfaces: A new approach to Brownian motion of atomic clusters on solid surfaces is
developed. The main topic discussed is the dependence of the diffusion
coefficient on the fit between the surface static potential and the internal
cluster configuration. It is shown this dependence is non-monotonous, which is
the essence of the so-called resonant diffusion. Assuming quicker inner motion
of the cluster than its translation, adiabatic separation of these variables is
possible and a relatively simple expression for the diffusion coefficient is
obtained. In this way, the role of cluster vibrations is accounted for, thus
leading to a more complex resonance in the cluster surface mobility. | cond-mat_stat-mech |
Anomalous spin frustration enforced by a magnetoelastic coupling in the
mixed-spin Ising model on decorated planar lattices: The mixed spin-1/2 and spin-S Ising model on a decorated planar lattice
accounting for lattice vibrations of decorating atoms is treated by making use
of the canonical coordinate transformation, the decoration-iteration
transformation, and the harmonic approximation. It is shown that the
magnetoelastic coupling gives rise to an effective single-ion anisotropy and
three-site four-spin interaction, which are responsible for the anomalous spin
frustration of the decorating spins in virtue of a competition with the
equilibrium nearest-neighbor exchange interaction between the nodal and
decorating spins. The ground-state and finite-temperature phase diagrams are
constructed for the particular case of the mixed spin-1/2 and spin-1 Ising
model on a decorated square lattice for which thermal dependencies of the
spontaneous magnetization and specific heat are also examined in detail. It is
evidenced that a sufficiently strong magnetoelastic coupling leads to a
peculiar coexistence of the antiferromagnetic long-range order of the nodal
spins with the disorder of the decorating spins within the frustrated
antiferromagnetic phase, which may also exhibit double reentrant phase
transitions. The investigated model displays a variety of temperature
dependencies of the total specific heat, which may involve in its magnetic part
one or two logarithmic divergences apart from one or two additional round
maxima superimposed on a standard thermal dependence of the lattice part of the
specific heat. | cond-mat_stat-mech |
Dissolution in a field: We study the dissolution of a solid by continuous injection of reactive
``acid'' particles at a single point, with the reactive particles undergoing
biased diffusion in the dissolved region. When acid encounters the substrate
material, both an acid particle and a unit of the material disappear. We find
that the lengths of the dissolved cavity parallel and perpendicular to the bias
grow as t^{2/(d+1)} and t^{1/(d+1)}, respectively, in d-dimensions, while the
number of reactive particles within the cavity grows as t^{2/(d+1)}. We also
obtain the exact density profile of the reactive particles and the relation
between this profile and the motion of the dissolution boundary. The extension
to variable acid strength is also discussed. | cond-mat_stat-mech |
A Fractional entropy in Fractal phase space: properties and
characterization: A two parameter generalization of Boltzmann-Gibbs-Shannon entropy based on
natural logarithm is introduced. The generalization of the Shannon-Kinchinn
axioms corresponding to the two parameter entropy is proposed and verified. We
present the relative entropy, Jensen-Shannon divergence measure and check their
properties. The Fisher information measure, relative Fisher information and the
Jensen-Fisher information corresponding to this entropy are also derived. The
canonical distribution maximizing this entropy is derived and is found to be in
terms of the Lambert's W function. Also the Lesche stability and the
thermodynamic stability conditions are verified. Finally we propose a
generalization of a complexity measure and apply it to a two level system and a
system obeying exponential distribution. The results are compared with the
corresponding ones obtained using a similar measure based on the Shannon
entropy. | cond-mat_stat-mech |
Dissipative Quantum Systems and the Heat Capacity Enigma: We present a detailed study of the quantum dissipative dynamics of a charged
particle in a magnetic field. Our focus of attention is the effect of
dissipation on the low- and high-temperature behavior of the specific heat at
constant volume. After providing a brief overview of two distinct approaches to
the statistical mechanics of dissipative quantum systems, viz., the ensemble
approach of Gibbs and the quantum Brownian motion approach due to Einstein, we
present exact analyses of the specific heat. While the low-temperature
expressions for the specific heat, based on the two approaches, are in
conformity with power-law temperature-dependence, predicted by the third law of
thermodynamics, and the high-temperature expressions are in agreement with the
classical equipartition theorem, there are surprising differences between the
dependencies of the specific heat on different parameters in the theory, when
calculations are done from these two distinct methods. In particular, we find
puzzling influences of boundary-confinement and the bath-induced spectral
cutoff frequency. Further, when it comes to the issue of approach to
equilibrium, based on the Einstein method, the way the asymptotic limit (time
going to infinity) is taken, seems to assume significance. | cond-mat_stat-mech |
A constrained stochastic state selection method applied to quantum spin
systems: We describe a further development of the stochastic state selection method,
which is a kind of Monte Carlo method we have proposed in order to numerically
study large quantum spin systems. In the stochastic state selection method we
make a sampling which is simultaneous for many states. This feature enables us
to modify the method so that a number of given constraints are satisfied in
each sampling. In this paper we discuss this modified stochastic state
selection method that will be called the constrained stochastic state selection
method in distinction from the previously proposed one (the conventional
stochastic state selection method) in this paper. We argue that in virtue of
the constrained sampling some quantities obtained in each sampling become more
reliable, i.e. their statistical fluctuations are less than those from the
conventional stochastic state selection method. In numerical calculations of
the spin-1/2 quantum Heisenberg antiferromagnet on a 36-site triangular lattice
we explicitly show that data errors in our estimation of the ground state
energy are reduced. Then we successfully evaluate several low-lying energy
eigenvalues of the model on a 48-site lattice. Our results support that this
system can be described by the theory based on the spontaneous symmetry
breaking in the semiclassical Neel ordered antiferromagnet. | cond-mat_stat-mech |
Dissipative Effects in Nonlinear Klein-Gordon Dynamics: We consider dissipation in a recently proposed nonlinear Klein-Gordon
dynamics that admits soliton-like solutions of the power-law form
$e_q^{i(kx-wt)}$, involving the $q$-exponential function naturally arising
within the nonextensive thermostatistics [$e_q^z \equiv [1+(1-q)z]^{1/(1-q)}$,
with $e_1^z=e^z$]. These basic solutions behave like free particles, complying,
for all values of $q$, with the de Broglie-Einstein relations $p=\hbar k$,
$E=\hbar \omega$ and satisfying a dispersion law corresponding to the
relativistic energy-momentum relation $E^2 = c^2p^2 + m^2c^4 $. The dissipative
effects explored here are described by an evolution equation that can be
regarded as a nonlinear version of the celebrated telegraphists equation,
unifying within one single theoretical framework the nonlinear Klein-Gordon
equation, a nonlinear Schroedinger equation, and the power-law diffusion
(porous media) equation. The associated dynamics exhibits physically appealing
soliton-like traveling solutions of the $q$-plane wave form with a complex
frequency $\omega$ and a $q$-Gaussian square modulus profile. | cond-mat_stat-mech |
Collective excitations of a periodic Bose condensate in the Wannier
representation: We study the dispersion relation of the excitations of a dilute Bose-Einstein
condensate confined in a periodic optical potential and its Bloch oscillations
in an accelerated frame. The problem is reduced to one-dimensionality through a
renormalization of the s-wave scattering length and the solution of the
Bogolubov - de Gennes equations is formulated in terms of the appropriate
Wannier functions. Some exact properties of a periodic one-dimensional
condensate are easily demonstrated: (i) the lowest band at positive energy
refers to phase modulations of the condensate and has a linear dispersion
relation near the Brillouin zone centre; (ii) the higher bands arise from the
superposition of localized excitations with definite phase relationships; and
(iii) the wavenumber-dependent current under a constant force in the
semiclassical transport regime vanishes at the zone boundaries. Early results
by J. C. Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron
energy bands are used to specify the conditions under which the Wannier
functions may be approximated by on-site tight-binding orbitals of harmonic-
oscillator form. In this approximation the connections between the low-lying
excitations in a lattice and those in a harmonic well are easily visualized.
Analytic results are obtained in the tight-binding scheme and are illustrated
with simple numerical calculations for the dispersion relation and
semiclassical transport in the lowest energy band, at values of the system
parameters which are relevant to experiment. | cond-mat_stat-mech |
Phase diagram of asymmetric Fermi gas across Feshbach resonance: We study the phase diagram of the dilute two-component Fermi gas at zero
temperature as a function of the polarization and coupling strength. We map out
the detailed phase separations between superfluid and normal states near the
Feshbach resonance. We show that there are three different coexistence of
superfluid and normal phases corresponding to phase separated states between:
(I) the partially polarized superfluid and the fully polarized normal phases,
(II) the unpolarized superfluid and the fully polarized normal phases and (III)
the unpolarized superfluid and the partially polarized normal phases from
strong-coupling BEC side to weak-coupling BCS side. For pairing between two
species, we found this phase separation regime gets wider and moves toward the
BEC side for the majority species are heavier but shifts to BCS side and
becomes narrow if they are lighter. | cond-mat_stat-mech |
A complete theory of low-energy phase diagrams for two-dimensional
turbulence steady states and equilibria: For the 2D Euler equations and related models of geophysical flows, minima of
energy--Casimir variational problems are stable steady states of the equations
(Arnol'd theorems). The same variational problems also describe sets of
statistical equilibria of the equations. In this paper, we make use of
Lyapunov--Schmidt reduction in order to study the bifurcation diagrams for
these variational problems, in the limit of small energy or, equivalently, of
small departure from quadratic Casimir functionals. We show a generic
occurrence of phase transitions, either continuous or discontinuous. We derive
the type of phase transitions for any domain geometry and any model analogous
to the 2D Euler equations. The bifurcations depend crucially on a_4, the
quartic coefficient in the Taylor expansion of the Casimir functional around
its minima. Note that a_4 can be related to the fourth moment of the vorticity
in the statistical mechanics framework. A tricritical point (bifurcation from a
continuous to a discontinuous phase transition) often occurs when a_4 changes
sign. The bifurcations depend also on possible constraints on the variational
problems (circulation, energy). These results show that the analytical results
obtained with quadratic Casimir functionals by several authors are non-generic
(not robust to a small change in the parameters). | cond-mat_stat-mech |
Energy fluctuations of a Brownian particle freely moving in a liquid: We study the statistical properties of the variation of the kinetic energy of
a spherical Brownian particle that freely moves in an incompressible fluid at
constant temperature. Based on the underdamped version of the generalized
Langevin equation that includes the inertia of both the particle and the
displaced fluid, we derive an analytical expression for the probability density
function of such a kinetic energy variation during an arbitrary time interval,
which exactly amounts to the energy exchanged with the fluid in absence of
external forces. We also determine all the moments of this probability
distribution, which can be fully expressed in terms of a function that is
proportional to the velocity autocorrelation function of the particle. The
derived expressions are verified by means of numerical simulations of the
stochastic motion of a particle in a viscous liquid with hydrodynamic backflow
for representative values of the time-scales of the system. Furthermore, we
also investigate the effect of viscoelasticity on the statistics of the kinetic
energy variation of the particle, which reveals the existence of three distinct
regimes of the energy exchange process depending on the values of the
viscoelastic parameters of the fluid. | cond-mat_stat-mech |
Resonant Activation Phenomenon for Non-Markovian Potential-Fluctuation
Processes: We consider a generalization of the model by Doering and Gadoua to
non-Markovian potential-switching generated by arbitrary renewal processes. For
the Markovian switching process, we extend the original results by Doering and
Gadoua by giving a complete description of the absorption process. For all
non-Markovian processes having the first moment of the waiting time
distributions, we get qualitatively the same results as in the Markovian case.
However, for distributions without the first moment, the mean first passage
time curves do not exhibit the resonant activation minimum. We thus come to the
conjecture that the generic mechanism of the resonant activation fails for
fluctuating processes widely deviating from Markovian. | cond-mat_stat-mech |
Broken Ergodicity in classically chaotic spin systems: A one dimensional classically chaotic spin chain with asymmetric coupling and
two different inter-spin interactions, nearest neighbors and all-to-all, has
been considered. Depending on the interaction range, dynamical properties, as
ergodicity and chaoticity are strongly different. Indeed, even in presence of
chaoticity, the model displays a lack of ergodicity only in presence of all to
all interaction and below an energy threshold, that persists in the
thermodynamical limit. Energy threshold can be found analytically and results
can be generalized for a generic XY model with asymmetric coupling. | cond-mat_stat-mech |
Computer simulation of fluid phase transitions: The task of accurately locating fluid phase boundaries by means of computer
simulation is hampered by problems associated with sampling both coexisting
phases in a single simulation run. We explain the physical background to these
problems and describe how they can be tackled using a synthesis of biased Monte
Carlo sampling and histogram extrapolation methods, married to a standard fluid
simulation algorithm. It is demonstrated that the combined approach provides a
powerful method for tracing fluid phase boundaries. | cond-mat_stat-mech |
Efficiency fluctuations of small machines with unknown losses: The efficiency statistics of a small thermodynamic machine has been recently
investigated assuming that the total dissipation was a linear combination of
two currents: the input and output currents. Here, we relax this standard
assumption and reconsider the question of the efficiency fluctuations for a
machine involving three different processes, first in full generality and
second for two different examples. Since the third process may not be
measurable and/or may decrease the machine efficiency, our motivation is to
study the effect of unknown losses in small machines. | cond-mat_stat-mech |
Nonequilibrium work statistics of an Aharonov-Bohm flux: We investigate the statistics of work performed on a noninteracting electron
gas confined into a ring as a threaded magnetic field is turned on. For an
electron gas initially prepared in a grand canonical state it is demonstrated
that the Jarzynski equality continues to hold in this case, with the free
energy replaced by the grand potential. The work distribution displays a marked
dependence on the temperature. While in the classical (high temperature)
regime, the work probability density function follows a Gaussian distribution
and the free energy difference entering the Jarzynski equality is null, the
free energy difference is finite in the quantum regime, and the work
probability distribution function becomes multimodal. We point out the
dependence of the work statistics on the number of electrons composing the
system. | cond-mat_stat-mech |
Preroughening transitions in a model for Si and Ge (001) type crystal
surfaces: The uniaxial structure of Si and Ge (001) facets leads to nontrivial
topological properties of steps and hence to interesting equilibrium phase
transitions. The disordered flat phase and the preroughening transition can be
stabilized without the need for step-step interactions. A model describing this
is studied numerically by transfer matrix type finite-size-scaling of interface
free energies. Its phase diagram contains a flat, rough, and disordered flat
phase, separated by roughening and preroughening transition lines. Our estimate
for the location of the multicritical point where the preroughening line merges
with the roughening line, predicts that Si and Ge (001) undergo preroughening
induced simultaneous deconstruction transitions. | cond-mat_stat-mech |
First-order phase transition in $1d$ Potts model with long-range
interactions: The first-order phase transition in the one-dimensional $q$-state Potts model
with long-range interactions decaying with distance as $1/r^{1+\sigma}$ has
been studied by Monte Carlo numerical simulations for $0 < \sigma \le 1$ and
integer values of $q > 2$. On the basis of finite-size scaling analysis of
interface free energy $\Delta F_L$, specific heat and Binder's fourth order
cumulant, we obtain the first-order transition which occurs for $\sigma$ below
a threshold value $\sigma_c(q)$. | cond-mat_stat-mech |
Reply to the comment on "Avalanches and Non-Gaussian Fluctuations of the
Global Velocity of Imbibition Fronts": In [R. Planet, S. Santucci and J. Ortin, Phys. Rev. Lett. 102, 094502
(2009)], we reported that both the size and duration of the global avalanches
observed during a forced imbibition process follow power law distributions with
cut-offs. Following a comment by G. Pruessner, we discuss here the right
procedure to perfom, in order to extract reliable exponents characterising
those pdf's. | cond-mat_stat-mech |
An exact solution of the inelastic Boltzmann equation for the Couette
flow with uniform heat flux: In the steady Couette flow of a granular gas the sign of the heat flux
gradient is governed by the competition between viscous heating and inelastic
cooling. We show from the Boltzmann equation for inelastic Maxwell particles
that a special class of states exists where the viscous heating and the
inelastic cooling exactly compensate each other at every point, resulting in a
uniform heat flux. In this state the (reduced) shear rate is enslaved to the
coefficient of restitution $\alpha$, so that the only free parameter is the
(reduced) thermal gradient $\epsilon$. It turns out that the reduced moments of
order $k$ are polynomials of degree $k-2$ in $\epsilon$, with coefficients that
are nonlinear functions of $\alpha$. In particular, the rheological properties
($k=2$) are independent of $\epsilon$ and coincide exactly with those of the
simple shear flow. The heat flux ($k=3$) is linear in the thermal gradient
(generalized Fourier's law), but with an effective thermal conductivity
differing from the Navier--Stokes one. In addition, a heat flux component
parallel to the flow velocity and normal to the thermal gradient exists. The
theoretical predictions are validated by comparison with direct Monte Carlo
simulations for the same model. | cond-mat_stat-mech |
Escape from bounded domains driven by multi-variate $α$-stable
noises: In this paper we provide an analysis of a mean first passage time problem of
a random walker subject to a bi-variate $\alpha$-stable L\'evy type noise from
a 2-dimensional disk. For an appropriate choice of parameters the mean first
passage time reveals non-trivial, non-monotonous dependence on the stability
index $\alpha$ describing jumps' length asymptotics both for spherical and
Cartesian L\'evy flights. Finally, we study escape from $d$-dimensional
hyper-sphere showing that $d$-dimensional escape process can be used to
discriminate between various types of multi-variate $\alpha$-stable noises,
especially spherical and Cartesian L\'evy flights. | cond-mat_stat-mech |
A Cellular Automaton Model for the Traffic Flow in Bogota: In this work we propose a car cellular automaton model that reproduces the
experimental behavior of traffic flows in Bogot\'a. Our model includes three
elements: hysteresis between the acceleration and brake gaps, a delay time in
the acceleration, and an instantaneous brake. The parameters of our model were
obtained from direct measurements inside a car on motorways in Bogot\'a. Next,
we simulated with this model the flux-density fundamental diagram for a
single-lane traffic road and compared it with experimental data. Our
simulations are in very good agreement with the experimental measurements, not
just in the shape of the fundamental diagram, but also in the numerical values
for both the road capacity and the density of maximal flux. Our model
reproduces, too, the qualitative behavior of shock waves. In addition, our work
identifies the periodic boundary conditions as the source of false peaks in the
fundamental diagram, when short roads are simulated, that have been also found
in previous works. The phase transition between free and congested traffic is
also investigated by computing both the relaxation time and the order
parameter. Our work shows how different the traffic behavior from one city to
another can be, and how important is to determine the model parameters for each
city. | cond-mat_stat-mech |
Universality in volume law entanglement of pure quantum states: A pure quantum state can fully describe thermal equilibrium as long as one
focuses on local observables. Thermodynamic entropy can also be recovered as
the entanglement entropy of small subsystems. When the size of the subsystem
increases, however, quantum correlations break the correspondence and cause a
correction to this simple volume-law. To elucidate the size dependence of the
entanglement entropy is of essential importance in linking quantum physics with
thermodynamics, and in addressing recent experiments in ultra-cold atoms. Here
we derive an analytic formula of the entanglement entropy for a class of pure
states called cTPQ states representing thermal equilibrium. We further find
that our formula applies universally to any sufficiently scrambled pure states
representing thermal equilibrium, i.e., general energy eigenstates of
non-integrable models and states after quantum quenches. Our universal formula
can be exploited as a diagnostic of chaotic systems; we can distinguish
integrable models from chaotic ones and detect many-body localization with high
accuracy. | cond-mat_stat-mech |
Nonequilibrium Dynamic Phase transitions in ferromagnetic systems: Some
new phenomena: The nonequilibrium dynamic phase transition in ferromagnetic systems is
reviewed. Very recent results of dynamic transition in kinetic Ising model and
that in Heisenberg ferromagnet is discussed. | cond-mat_stat-mech |
Levy flights and Levy -Schroedinger semigroups: We analyze two different confining mechanisms for L\'{e}vy flights in the
presence of external potentials. One of them is due to a conservative force in
the corresponding Langevin equation. Another is implemented by
Levy-Schroedinger semigroups which induce so-called topological Levy processes
(Levy flights with locally modified jump rates in the master equation). Given a
stationary probability function (pdf) associated with the Langevin-based
fractional Fokker-Planck equation, we demonstrate that generically there exists
a topological L\'{e}vy process with the very same invariant pdf and in the
reverse. | cond-mat_stat-mech |
Exact Analysis of ESR Shift in the Spin-1/2 Heisenberg Antiferromagnetic
Chain: A systematic perturbation theory is developed for the ESR shift and is
applied to the spin-1/2 Heisenberg chain. Using the Bethe ansatz technique, we
exactly analyze the resonance shift in the first order of perturbative
expansion with respect to an anisotropic exchange interaction. Exact result for
the whole range of temperature and magnetic field, as well as asymptotic
behavior in the low-temperature limit are presented. The obtained g-shift
strongly depends on magnetic fields at low temperature, showing a significant
deviation from the previous classical result. | cond-mat_stat-mech |
Dynamical phase diagram of the dc-driven underdamped Frenkel-Kontorova
chain: Multistep dynamical phase transition from the locked to the running state of
atoms in response to a dc external force is studied by MD simulations of the
generalized Frenkel-Kontorova model in the underdamped limit. We show that the
hierarchy of transition recently reported [Braun et al, Phys. Rev. Lett. 78,
1295 (1997)] strongly depends on the value of the friction constant. A simple
phenomenological explanation for the friction dependence of the various
critical forces separating intermediate regimes is given. | cond-mat_stat-mech |
Thermodynamic and magnetic properties of the Ising model with
nonmagnetic impurities: We consider a system of Ising spins s=1/2 with nonmagnetic impurities with
charge associated with pseudospin S=1. The charge density is fixed pursuant to
the concentration n. Analysis of the thermodynamic properties in the
one-dimensional case showed the presence of so-called pseudotransitions at the
boundaries between the staggered charge ordering and (anti)ferromagnetic
ordering. In the case of n=0, a "1st order" pseudotransition was discovered.
This type of pseudotransition is inherent for a series of other one-dimensional
frustrated models. However, for n != 0 we discovered a new type of "2nd order"
pseudotransition, which had not previously been observed in other systems. | cond-mat_stat-mech |
Description of the dynamics of a random chain with rigid constraints in
the path integral framework: In this work we discuss the dynamics of a three dimensional chain which is
described by generalized nonlinear sigma model The formula of the probability
distribution of two topologically entangled chain is provided. The interesting
case of a chain which can form only discrete angles with respect to the
$z-$axis is also presented. | cond-mat_stat-mech |
Chiral exponents in frustrated spin models with noncollinear ordering: We compute the chiral critical exponents for the chiral transition in
frustrated two- and three-component spin systems with noncollinear order, such
as stacked triangular antiferromagnets (STA). For this purpose, we calculate
and analyze the six-loop field-theoretical expansion of the
renormalization-group function associated with the chiral operator. The results
are in satisfactory agreement with those obtained in the recent experiment on
the XY STA CsMnBr_3 reported by V. P. Plakhty et al., Phys. Rev. Lett. 85, 3942
(2000), providing further support for the continuous nature of the chiral
transition. | cond-mat_stat-mech |
Thermodynamics of interacting hard rods on a lattice: We present an exact derivation of the isobaric partition function of lattice
hard rods with arbitrary nearest neighbor interactions. Free energy and all
thermodynamics functions are derived accordingly and they written in a form
that is a suitable for numerical implementation. As an application, we have
considered lattice rods with pure hard core interactions, rods with long range
gravitational attraction and finally a charged hard rods with charged
boundaries (Bose gas), a model that is relevant for studying several phenomena
such as charge regulation, ionic liquids near charged interfaces, and an array
of charged smectic layers or lipid multilayers. In all cases, thermodynamic
analysis have been done numerically using the Broyden algorithm. | cond-mat_stat-mech |
Rare events in stochastic processes with sub-exponential distributions
and the Big Jump principle: Rare events in stochastic processes with heavy-tailed distributions are
controlled by the big jump principle, which states that a rare large
fluctuation is produced by a single event and not by an accumulation of
coherent small deviations. The principle has been rigorously proved for sums of
independent and identically distributed random variables and it has recently
been extended to more complex stochastic processes involving L\'evy
distributions, such as L\'evy walks and the L\'evy-Lorentz gas, using an
effective rate approach. We review the general rate formalism and we extend its
applicability to continuous time random walks and to the Lorentz gas, both with
stretched exponential distributions, further enlarging its applicability. We
derive an analytic form for the probability density functions for rare events
in the two models, which clarify specific properties of stretched exponentials. | cond-mat_stat-mech |
Energy Landscape and Isotropic Tensile Strength of n-Alkane Glasses: Submission has been withdrawn due to copyright issues. | cond-mat_stat-mech |
Scaling of wetting and pre-wetting transitions on nano-patterned walls: We consider a nano-patterned planar wall consisting of a periodic array of
stripes of width $L$, which are completely wet by liquid (contact angle
$\theta=0$), separated by regions of width $D$ which are completely dry
(contact angle $\theta=\pi)$. Using microscopic Density Functional Theory we
show that in the presence of long-ranged dispersion forces, the wall-gas
interface undergoes a first-order wetting transition, at bulk coexistence, as
the separation $D$ is reduced to a value $D_w\propto\ln L$, induced by the
bridging between neighboring liquid droplets. Associated with this is a line of
pre-wetting transitions occurring off coexistence. By varying the stripe width
$L$ we show that the pre-wetting line shows universal scaling behaviour and
data collapse. This verifies predictions based on mesoscopic models for the
scaling properties associated with finite-size effects at complete wetting
including the logarithmic singular contribution to the surface free-energy. | cond-mat_stat-mech |
Capturing exponential variance using polynomial resources: applying
tensor networks to non-equilibrium stochastic processes: Estimating the expected value of an observable appearing in a non-equilibrium
stochastic process usually involves sampling. If the observable's variance is
high, many samples are required. In contrast, we show that performing the same
task without sampling, using tensor network compression, efficiently captures
high variances in systems of various geometries and dimensions. We provide
examples for which matching the accuracy of our efficient method would require
a sample size scaling exponentially with system size. In particular, the high
variance observable $\mathrm{e}^{-\beta W}$, motivated by Jarzynski's equality,
with $W$ the work done quenching from equilibrium at inverse temperature
$\beta$, is exactly and efficiently captured by tensor networks. | cond-mat_stat-mech |
Swarming in disordered environments: The emergence of collective motion, also known as flocking or swarming, in
groups of moving individuals who orient themselves using only information from
their neighbors is a very general phenomenon that is manifested at multiple
spatial and temporal scales. Swarms that occur in natural environments
typically have to contend with spatial disorder such as obstacles that hinder
an individual's motion or communication with neighbors. We study swarming
particles, with both aligning and repulsive interactions, on percolated
networks where topological disorder is modeled by the random removal of lattice
bonds. We find that an infinitesimal amount of disorder can completely suppress
swarming for particles that utilize only alignment interactions suggesting that
alignment alone is insufficient. The addition of repulsive forces between
particles produces a critical phase transition from a collectively moving swarm
to a disordered gas-like state. This novel phase transition is entirely driven
by the amount of topological disorder in the particles environment and displays
critical features that are similar to those of 2D percolation, while occurring
at a value of disorder that is far from the percolation critical point. | cond-mat_stat-mech |
Statistics of interfacial fluctuations of radially growing clusters: The dynamics of fluctuating radially growing interfaces is approached using
the formalism of stochastic growth equations on growing domains. This framework
reveals a number of dynamic features arising during surface growth. For fast
growth, dilution, which spatially reorders the incoming matter, is responsible
for the transmission of correlations. Its effects include the erasing of memory
with respect to the initial condition, a partial attenuation of geometrically
originated instabilities, and the restoring of universality in some special
cases in which the critical exponents depend on the parameters of the equation
of motion. In this sense, dilution rends the dynamics more similar to the usual
one of planar systems. This fast growth regime is also characterized by the
spatial decorrelation of the interface, which in the case of radially growing
interfaces naturally originates rapid roughening and scale dependent
fractality, and suggests the advent of a self-similar fractal dimension. The
center of mass fluctuations of growing clusters are also studied, and our
analysis suggests the possible non-applicability of usual scalings to the long
range surface fluctuations of the radial Eden model. In fact, our study points
to the fact that this model belongs to a dilution-free universality class. | cond-mat_stat-mech |
Edwards-like statistical mechanical description of the parking lot model
for vibrated granular materials: We apply the statistical mechanical approach based on the ``flat'' measure
proposed by Edwards and coworkers to the parking lot model, a model that
reproduces the main features of the phenomenology of vibrated granular
materials. We first build the flat measure for the case of vanishingly small
tapping strength and then generalize the approach to finite tapping strengths
by introducing a new ``thermodynamic'' parameter, the available volume for
particle insertion, in addition to the particle density. This description is
able to take into account the various memory effects observed in vibrated
granular media. Although not exact, the approach gives a good description of
the behavior of the parking-lot model in the regime of slow compaction. | cond-mat_stat-mech |
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