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Spontaneous Breaking of Translational Invariance and Spatial
Condensation in Stationary States on a Ring: II. The Charged System and the
Two-component Burgers Equations: We further study the stochastic model discussed in Ref.[2] in which positive
and negative particles diffuse in an asymmetric, CP invariant way on a ring.
The positive particles hop clockwise, the negative counter-clockwise and
oppositely-charged adjacent particles may swap positions. We extend the
analysis of this model to the case when the densities of the charged particles
are not the same. The mean-field equations describing the model are coupled
nonlinear differential equations that we call the two-component Burgers
equations. We find roundabout weak solutions of these equations. These
solutions are used to describe the properties of the stationary states of the
stochastic model. The values of the currents and of various two-point
correlation functions obtained from Monte-Carlo simulations are compared with
the mean-field results. Like in the case of equal densities, one finds a pure
phase, a mixed phase and a disordered phase. | cond-mat_stat-mech |
Statistical Properties of Contact Maps: A contact map is a simple representation of the structure of proteins and
other chain-like macromolecules. This representation is quite amenable to
numerical studies of folding. We show that the number of contact maps
corresponding to the possible configurations of a polypeptide chain of N amino
acids, represented by (N-1)-step self avoiding walks on a lattice, grows
exponentially with N for all dimensions D>1. We carry out exact enumerations in
D=2 on the square and triangular lattices for walks of up to 20 steps and
investigate various statistical properties of contact maps corresponding to
such walks. We also study the exact statistics of contact maps generated by
walks on a ladder. | cond-mat_stat-mech |
The weighted random graph model: We introduce the weighted random graph (WRG) model, which represents the
weighted counterpart of the Erdos-Renyi random graph and provides fundamental
insights into more complicated weighted networks. We find analytically that the
WRG is characterized by a geometric weight distribution, a binomial degree
distribution and a negative binomial strength distribution. We also
characterize exactly the percolation phase transitions associated with edge
removal and with the appearance of weighted subgraphs of any order and
intensity. We find that even this completely null model displays a percolation
behavior similar to what observed in real weighted networks, implying that edge
removal cannot be used to detect community structure empirically. By contrast,
the analysis of clustering successfully reveals different patterns between the
WRG and real networks. | cond-mat_stat-mech |
Truncations of Random Orthogonal Matrices: Statistical properties of non--symmetric real random matrices of size $M$,
obtained as truncations of random orthogonal $N\times N$ matrices are
investigated. We derive an exact formula for the density of eigenvalues which
consists of two components: finite fraction of eigenvalues are real, while the
remaining part of the spectrum is located inside the unit disk symmetrically
with respect to the real axis. In the case of strong non--orthogonality,
$M/N=$const, the behavior typical to real Ginibre ensemble is found. In the
case $M=N-L$ with fixed $L$, a universal distribution of resonance widths is
recovered. | cond-mat_stat-mech |
Stochastic thermodynamics and modes of operation of a ribosome: a
network theoretic perspective: The ribosome is one of the largest and most complex macromolecular machines
in living cells. It polymerizes a protein in a step-by-step manner as directed
by the corresponding nucleotide sequence on the template messenger RNA (mRNA)
and this process is referred to as `translation' of the genetic message encoded
in the sequence of mRNA transcript. In each successful chemo-mechanical cycle
during the (protein) elongation stage, the ribosome elongates the protein by a
single subunit, called amino acid, and steps forward on the template mRNA by
three nucleotides called a codon. Therefore, a ribosome is also regarded as a
molecular motor for which the mRNA serves as the track, its step size is that
of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that
cycle serve as its fuel. What adds further complexity is the existence of
competing pathways leading to distinct cycles, branched pathways in each cycle
and futile consumption of fuel that leads neither to elongation of the nascent
protein nor forward stepping of the ribosome on its track. We investigate a
model formulated in terms of the network of discrete chemo-mechanical states of
a ribosome during the elongation stage of translation. The model is analyzed
using a combination of stochastic thermodynamic and kinetic analysis based on a
graph-theoretic approach. We derive the exact solution of the corresponding
master equations. We represent the steady state in terms of the cycles of the
underlying network and discuss the energy transduction processes. We identify
the various possible modes of operation of a ribosome in terms of its average
velocity and mean rate of GTP hydrolysis. We also compute entropy production as
functions of the rates of the interstate transitions and the thermodynamic cost
for accuracy of the translation process. | cond-mat_stat-mech |
On the existence of supersolid helium-4 monolayer films: Extensive Monte Carlo simulations of helium-4 monolayer films adsorbed on
weak substrates have been carried out, aimed at ascertaining the possible
occurrence of a quasi-two-dimensional supersolid phase. Only crystalline films
not registered with underlying substrates are considered. Numerical results
yield strong evidence that helium-4 will not form a supersolid film on {any}
substrate strong enough to stabilize a crystalline layer. On weaker substrates,
continuous growth of a liquid film takes place. | cond-mat_stat-mech |
Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment
of the Tonks Girardeau limit: Aiming at studying the emergence of Non-Equilibrium Steady States (NESS) in
quantum integrable models by means of an exact analytical method, we focus on
the Tonks-Girardeau or hard-core boson limit of the Lieb-Liniger model. We
consider the abrupt expansion of a gas from one half to the entire confining
box, a prototypical case of inhomogeneous quench, also known as "geometric
quench". Based on the exact calculation of quench overlaps, we develop an
analytical method for the derivation of the NESS by rigorously treating the
thermodynamic and large time and distance limit. Our method is based on complex
analysis tools for the derivation of the asymptotics of the many-body
wavefunction, does not make essential use of the effectively non-interacting
character of the hard-core boson gas and is sufficiently robust for
generalisation to the genuinely interacting case. | cond-mat_stat-mech |
Dissipative maps at the chaos threshold: Numerical results for the
single-site map: We numerically study, at the edge of chaos, the behaviour of the sibgle-site
map $x_{t+1}=x_t-x_t/(x_t^2+\gamma^2)$, where $\gamma$ is the map parameter. | cond-mat_stat-mech |
A perturbative path integral study of active and passive tracer
diffusion in fluctuating fields: We study the effective diffusion constant of a Brownian particle linearly
coupled to a thermally fluctuating scalar field. We use a path integral method
to compute the effective diffusion coefficient perturbatively to lowest order
in the coupling constant. This method can be applied to cases where the field
is affected by the particle (an active tracer), and cases where the tracer is
passive. Our results are applicable to a wide range of physical problems, from
a protein diffusing in a membrane to the dispersion of a passive tracer in a
random potential. In the case of passive diffusion in a scalar field, we show
that the coupling to the field can, in some cases, speed up the diffusion
corresponding to a form of stochastic resonance. Our results on passive
diffusion are also confirmed via a perturbative calculation of the probability
density function of the particle in a Fokker-Planck formulation of the problem.
Numerical simulations on simplified systems corroborate our results. | cond-mat_stat-mech |
Virtual potentials for feedback traps: The recently developed feedback trap can be used to create arbitrary virtual
potentials, to explore the dynamics of small particles or large molecules in
complex situations. Experimentally, feedback traps introduce several finite
time scales: there is a delay between the measurement of a particle's position
and the feedback response; the feedback response is applied for a finite update
time; and a finite camera exposure integrates motion. We show how to
incorporate such timing effects into the description of particle motion. For
the test case of a virtual quadratic potential, we give the first accurate
description of particle dynamics, calculating the power spectrum and variance
of fluctuations as a function of feedback gain, testing against simulations. We
show that for small feedback gains, the motion approximates that of a particle
in an ordinary harmonic potential. Moreover, if the potential is varied in
time, for example by varying its stiffness, the work that is calculated
approximates that done in an ordinary changing potential. The quality of the
approximation is set by the ratio of the update time of the feedback loop to
the relaxation time of motion in the virtual potential. | cond-mat_stat-mech |
Potts-Percolation-Gauss Model of a Solid: We study a statistical mechanics model of a solid. Neighboring atoms are
connected by Hookian springs. If the energy is larger than a threshold the
"spring" is more likely to fail, while if the energy is lower than the
threshold the spring is more likely to be alive. The phase diagram and
thermodynamic quantities, such as free energy, numbers of bonds and clusters,
and their fluctuations, are determined using renormalization-group and
Monte-Carlo techniques. | cond-mat_stat-mech |
Jamming versus Glass Transitions: Recent ideas based on the properties of assemblies of frictionless particles
in mechanical equilibrium provide a perspective of amorphous systems different
from that offered by the traditional approach originating in liquid theory. The
relation, if any, between these two points of view, and the relevance of the
former to the glass phase, has been difficult to ascertain. In this paper we
introduce a model for which both theories apply strictly: it exhibits on the
one hand an ideal glass transition and on the other `jamming' features
(fragility, soft modes) virtually identical to that of real systems. This
allows us to disentangle the different contents and domains of applicability of
the two physical phenomena. | cond-mat_stat-mech |
Computing solution space properties of combinatorial optimization
problems via generic tensor networks: We introduce a unified framework to compute the solution space properties of
a broad class of combinatorial optimization problems. These properties include
finding one of the optimum solutions, counting the number of solutions of a
given size, and enumeration and sampling of solutions of a given size. Using
the independent set problem as an example, we show how all these solution space
properties can be computed in the unified approach of generic tensor networks.
We demonstrate the versatility of this computational tool by applying it to
several examples, including computing the entropy constant for hardcore lattice
gases, studying the overlap gap properties, and analyzing the performance of
quantum and classical algorithms for finding maximum independent sets. | cond-mat_stat-mech |
Higgs and Goldstone modes in crystalline solids: In crystalline solids the acoustic phonon is known to be the
frequency-gapless Goldstone boson emerging from the spontaneous breaking of the
continuous Galilean symmetry induced by the crystal lattice. It has also been
described as the gauge boson that appears when the free electrons' Lagrangian
in the crystal is requested to be locally gauge invariant with respect to T(3),
the group of the infinitesimal spatial translations. However, the
non-Abelianity of T(3) makes the acoustic phonon a frequency-gapped mode, in
contradiction with its description as Goldstone boson. A different perspective
overcomes this contradiction. In fact, we show that both the acoustic and
optical phonon - the latter never appearing following the other two approaches
- emerge respectively as the gapless Goldstone (phase) and the gapped Higgs
(amplitude) fluctuation mode of an order parameter arising from the spontaneous
breaking of a global symmetry, without invoking the gauge principle. The
optical phonon's frequency-gap is present in all regimes, and it arises from a
mass-like term in the Lagrangian due to the Higgs mechanism itself. Instead, an
eventual acoustic phonon's frequency-gap appears only in the strong nonlinear
regime, and it is due to an anharmonic term, the same term arising from the
gauging of T(3), an approach which did not provide any description of the
optical phonon, though. In addition, the Higgs mechanism describes all the
phonon-phonon interactions, including a possible perturbation on the acoustic
phonon's frequency dispersion relation induced by the eventual optical phonon,
a peculiar behavior not described so far in these terms. | cond-mat_stat-mech |
Thermodynamic cost of external control: Artificial molecular machines are often driven by the periodic variation of
an external parameter. This external control exerts work on the system of which
a part can be extracted as output if the system runs against an applied load.
Usually, the thermodynamic cost of the process that generates the external
control is ignored. Here, we derive a refined second law for such small
machines that include this cost, which is, for example, generated by free
energy consumption of a chemical reaction that modifies the energy landscape
for such a machine. In the limit of irreversible control, this refined second
law becomes the standard one. Beyond this ideal limiting case, our analysis
shows that due to a new entropic term unexpected regimes can occur: The control
work can be smaller than the extracted work and the work required to generate
the control can be smaller than this control work. Our general inequalities are
illustrated by a paradigmatic three-state system. | cond-mat_stat-mech |
Component sizes in networks with arbitrary degree distributions: We give an exact solution for the complete distribution of component sizes in
random networks with arbitrary degree distributions. The solution tells us the
probability that a randomly chosen node belongs to a component of size s, for
any s. We apply our results to networks with the three most commonly studied
degree distributions -- Poisson, exponential, and power-law -- as well as to
the calculation of cluster sizes for bond percolation on networks, which
correspond to the sizes of outbreaks of SIR epidemic processes on the same
networks. For the particular case of the power-law degree distribution, we show
that the component size distribution itself follows a power law everywhere
below the phase transition at which a giant component forms, but takes an
exponential form when a giant component is present. | cond-mat_stat-mech |
Fluctuation-dissipation theorem for thermo-refractive noise: We introduce a simple prescription for calculating the spectra of thermal
fluctuations of temperature-dependent quantities of the form $\hat{\delta
T}(t)=\int d^3\vec{r} \delta T(\vec{r},t) q(\vec{r})$. Here $T(\vec{r}, t)$ is
the local temperature at location $\vec{r}$ and time $t$, and $q(\vec{r})$ is
an arbitrary function. As an example of a possible application, we compute the
spectrum of thermo-refractive coating noise in LIGO, and find a complete
agreement with the previous calculation of Braginsky, Gorodetsky and
Vyatchanin. Our method has computational advantage, especially for non-regular
or non-symmetric geometries, and for the cases where $q(\vec{r})$ is
non-negligible in a significant fraction of the total volume. | cond-mat_stat-mech |
Biochemical machines for the interconversion of mutual information and
work: We propose a physically-realisable biochemical device that is coupled to a
biochemical reservoir of mutual information, fuel molecules and a chemical
bath. Mutual information allows work to be done on the bath even when the fuel
molecules appear to be in equilibrium; alternatively, mutual information can be
created by driving from the fuel or the bath. The system exhibits diverse
behaviour, including a regime in which the information, despite increasing
during the reaction, enhances the extracted work. We further demonstrate that a
modified device can function without the need for external manipulation,
eliminating the need for a complex and potentially costly control. | cond-mat_stat-mech |
Computation of the Kolmogorov-Sinai entropy using statistitical
mechanics: Application of an exchange Monte Carlo method: We propose a method for computing the Kolmogorov-Sinai (KS) entropy of
chaotic systems. In this method, the KS entropy is expressed as a statistical
average over the canonical ensemble for a Hamiltonian with many ground states.
This Hamiltonian is constructed directly from an evolution equation that
exhibits chaotic dynamics. As an example, we compute the KS entropy for a
chaotic repeller by evaluating the thermodynamic entropy of a system with many
ground states. | cond-mat_stat-mech |
Kardar-Parisi-Zhang universality from soft gauge modes: The emergence of superdiffusive spin dynamics in integrable classical and
quantum magnets is well established by now, but there is no generally valid
theoretical explanation for this phenomenon. A fundamental difficulty is that
the hydrodynamic fluctuations of conserved quasiparticle modes are purely
diffusive. We argue that in isotropic integrable magnets, a complete
hydrodynamic description must include soft "gauge" degrees of freedom, that
arise from spontaneous breaking of the Bethe pseudovacuum symmetry. We show
that the coarse-grained time evolution of these modes lies in the
Kardar-Parisi-Zhang universality class of dynamics. | cond-mat_stat-mech |
Soft modes in Fermi liquids at arbitrary temperatures: We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in
particular to investigate the number and nature of soft modes in Fermi liquids,
both in the hydrodynamic and the collisionless regimes. In the hydrodynamic
regime we show that Fermi-liquid theory is consistent with Navier-Stokes
hydrodynamics at all temperatures. The soft modes are the ones familiar from
classical hydrodynamics that are controlled by the five conservation laws;
namely, two first-sound modes, two shear diffusion modes, and one heat
diffusion mode. These modes have a particle-like spectrum and are soft, or
scale invariant, at all temperatures. In the collisionless regime we show that
the entire single-particle distribution function is soft with a continuous part
of the spectrum. This continuous soft mode, which is well known but often not
emphasized, has important physical consequences, e.g., for certain quantum
phase transitions. In addition, there are the well known soft zero-sound
excitations that describe angular fluctuations of the Fermi surface; their
spectra are particle-like. They are unrelated to conservation laws, acquire a
mass at any nonzero temperature, and their number depends on the strength of
the quasiparticle interaction. We also discuss the fates of these two families
of soft modes as the temperature changes. With increasing temperature the size
of the collisionless regime shrinks, the damping of the modes grows, and
eventually all of the collisionless modes become overdamped. In their stead the
five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low
frequencies. The two families of soft modes are unrelated and have very
different physical origins.In charged Fermi liquids the first-sound modes in
the hydrodynamic regime and the l=0 zero-sound modes in the collisionless
regime get replaced by plasmons, all other modes remain soft. | cond-mat_stat-mech |
Cahn-Hilliard Theory for Unstable Granular Flows: A Cahn-Hilliard-type theory for hydrodynamic fluctuations is proposed that
gives a quantitative description of the slowly evolving spatial correlations
and structures in density and flow fields in the early stages of evolution of
freely cooling granular fluids. Two mechanisms for pattern selection and
structure formation are identified: unstable modes leading to density
clustering (compare spinodal decomposition), and selective noise reduction
(compare peneplanation in structural geology) leading to vortex structures. As
time increases, the structure factor for the density field develops a maximum,
which shifts to smaller wave numbers. This corresponds to an approximately
diffusively growing length scale for density clusters. The spatial velocity
correlations exhibit algebraic decay $\sim r^{-d}$ on intermediate length
scales. The theoretical predictions for spatial correlation functions and
structure factors agree well with molecular dynamics simulations of a system of
inelastic hard disks. | cond-mat_stat-mech |
Universal scaling relations for logarithmic-correction exponents: By the early 1960's advances in statistical physics had established the
existence of universality classes for systems with second-order phase
transitions and characterized these by critical exponents which are different
to the classical ones. There followed the discovery of (now famous) scaling
relations between the power-law critical exponents describing second-order
criticality. These scaling relations are of fundamental importance and now form
a cornerstone of statistical mechanics. In certain circumstances, such scaling
behaviour is modified by multiplicative logarithmic corrections. These are also
characterized by critical exponents, analogous to the standard ones. Recently
scaling relations between these logarithmic exponents have been established.
Here, the theories associated with these advances are presented and expanded
and the status of investigations into logarithmic corrections in a variety of
models is reviewed. | cond-mat_stat-mech |
Slowest relaxation mode of the partially asymmetric exclusion process
with open boundaries: We analyze the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process on a finite
lattice and with the most general open boundary conditions. We extend results
obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L.
Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We
determine the finite-size scaling of the spectral gap, which characterizes the
approach to stationarity at large times, in the low and high density regimes
and on the coexistence line. We observe boundary induced crossovers and discuss
possible interpretations of our results in terms of effective domain wall
theories. | cond-mat_stat-mech |
Taming chaos to sample rare events: the effect of weak chaos: Rare events in non-linear dynamical systems are difficult to sample because
of the sensitivity to perturbations of initial conditions and of complex
landscapes in phase space. Here we discuss strategies to control these
difficulties and succeed in obtainining an efficient sampling within a
Metropolis-Hastings Monte Carlo framework. After reviewing previous successes
in the case of strongly chaotic systems, we discuss the case of weakly chaotic
systems. We show how different types of non-hyperbolicities limit the
efficiency of previously designed sampling methods and we discuss strategies
how to account for them. We focus on paradigmatic low-dimensional chaotic
systems such as the logistic map, the Pomeau-Maneville map, and area-preserving
maps with mixed phase space. | cond-mat_stat-mech |
The Rotating Vicsek Model: Pattern Formation and Enhanced Flocking in
Chiral Active Matter: We generalize the Vicsek model to describe the collective behaviour of polar
circle swimmers with local alignment interactions. While the phase transition
leading to collective motion in 2D (flocking) occurs at the same interaction to
noise ratio as for linear swimmers, as we show, circular motion enhances the
polarization in the ordered phase (enhanced flocking) and induces secondary
instabilities leading to structure formation. Slow rotations result in phase
separation whereas fast rotations generate patterns which consist of phase
synchronized microflocks of controllable self-limited size. Our results defy
the viewpoint that monofrequent rotations form a rather trivial extension of
the Vicsek model and establish a generic route to pattern formation in chiral
active matter with possible applications to control coarsening and to design
rotating microflocks. | cond-mat_stat-mech |
From Boltzmann-Gibbs ensemble to generalized ensembles: We reconsider the Boltzmann-Gibbs statistical ensemble in thermodynamics
using the multinomial coefficient approach. We show that an ensemble is defined
by the determination of four statistical quantities, the element probabilities
$p_i$, the configuration probabilities $P_j$, the entropy $S$ and the extremum
constraints (EC). This distinction is of central importance for the
understanding of the conditions under which a microcanonical, canonical and
macrocanonical ensemble is defined. These three ensembles are characterized by
the conservation of their sizes. A variation of the ensemble size creates
difficulties in the definitions of the quadruplet $\{p_i, P_j, S, \mt{EC}\}$,
giving rise for a generalization of the Boltzmann-Gibbs formalism, such one as
introduced by Tsallis. We demonstrate that generalized thermodynamics represent
a transformation of ordinary thermodynamics in such a way that the energy of
the system remains conserved.
From our results it becomes evident that Tsallis's formalism is a very
specific generalization, however, not the only one. We also revisit the
Jaynes's Maximum Entropy Principle, showing that in general it can lead to
incorrect results and consider the appropriate corrections. | cond-mat_stat-mech |
Different critical behaviors in cubic to trigonal and tetragonal
perovskites: Perovskites like LaAlO3 (or SrTiO3) undergo displacive structural phase
transitions from a cubic crystal to a trigonal (or tetragonal) structure. For
many years, the critical exponents in both these types of transitions have been
fitted to those of the isotropic three-components Heisenberg model. However,
field theoretical calculations showed that the isotropic fixed point of the
renormalization group is unstable, and renormalization group iterations flow
either to a cubic fixed point or to a fluctuation-driven first-order
transition. Here we show that these two scenarios correspond to the cubic to
trigonal and to the cubic to tetragonal transitions, respectively. In both
cases, the critical behavior is described by slowly varying effective critical
exponents, which exhibit universal features. For the trigonal case, we predict
a crossover of the effective exponents from their Ising values to their cubic
values (which are close to the isotropic ones). For the tetragonal case, the
effective exponents can have the isotropic values over a wide temperature
range, before exhibiting large changes en route to the first-order transition.
New renormalization group calculations near the isotropic fixed point in three
dimensions are presented and used to estimate the effective exponents, and
dedicated experiments to test these predictions are proposed. Similar
predictions apply to cubic magnetic and ferroelectric systems. | cond-mat_stat-mech |
A Minimal Off-Lattice Model for Alpha-helical Proteins: A minimal off-lattice model for alpha-helical proteins is presented. It is
based on hydrophobicity forces and sequence independent local interactions. The
latter are chosen so as to favor the formation of alpha-helical structure. They
model chirality and alpha-helical hydrogen bonding. The global structures
resulting from the competition between these forces are studied by means of an
efficient Monte Carlo method. The model is tested on two sequences of length
N=21 and 33 which are intended to form 2- and 3-helix bundles, respectively.
The local structure of our model proteins is compared to that of real
alpha-helical proteins, and is found to be very similar. The two sequences
display the desired numbers of helices in the folded phase. Only a few
different relative orientations of the helices are thermodynamically allowed.
Our ability to investigate the thermodynamics relies heavily upon the
efficiency of the used algorithm, simulated tempering; in this Monte Carlo
approach, the temperature becomes a fluctuating variable, enabling the crossing
of free-energy barriers. | cond-mat_stat-mech |
Tagged Particle Correlations in the Asymmetric Simple Exclusion Process:
Finite Size Effects: We study finite size effects in the variance of the displacement of a tagged
particle in the stationary state of the Asymmetric Simple Exclusion Process
(ASEP) on a ring of size $L$. The process involves hard core particles
undergoing stochastic driven dynamics on a lattice. The variance of the
displacement of the tagged particle, averaged with respect to an initial
stationary ensemble and stochastic evolution, grows linearly with time at both
small and very large times. We find that at intermediate times, it shows
oscillations with a well defined size-dependent period. These oscillations
arise from sliding density fluctuations (SDF) in the stationary state with
respect to the drift of the tagged particle, the density fluctuations being
transported through the system by kinematic waves. In the general context of
driven diffusive systems, both the Edwards-Wilkinson (EW) and the
Kardar-Parisi-Zhang (KPZ) fixed points are unstable with respect to the SDF
fixed point, a flow towards which is generated on adding a gradient term to the
EW and the KPZ time-evolution equation. We also study tagged particle
correlations for a fixed initial configuration, drawn from the stationary
ensemble, following earlier work by van Beijeren. We find that the time
dependence of this correlation is determined by the dissipation of the density
fluctuations. We show that an exactly solvable linearized model captures the
essential qualitative features seen in the finite size effects of the tagged
particle correlations in the ASEP. Moreover, this linearized model also
provides an exact coarse-grained description of two other microscopic models. | cond-mat_stat-mech |
Specific heat anomalies of small quantum systems subjected to finite
baths: We have studied the specific heat of the $(N_S+N_B)$ model for an $N_S$-body
harmonic oscillator (HO) system which is strongly coupled to an $N_B$-body HO
bath without dissipation. The system specific heat of $C_S(T)$ becomes $N_S
k_B$ at $T \rightarrow \infty$ and vanishes at $T = 0$ in accordance with the
third law of thermodynamics. The calculated $C_S(T)$ at low temperatures is not
proportional to $N_S$ and shows an anomalous temperature dependence, strongly
depending on $N_S$, $N_B$ and the system-bath coupling. In particular at very
low (but finite) temperatures, it may become {\it negative} for a strong
system-bath coupling, which is in contrast with {\it non-negative} specific
heat of an HO system with $N_S=1$ reported by G-L. Ingold, P. H\"{a}nggi and P.
Talkner [Phys. Rev. E {\bf 79}, 061105 (2005)]. Our calculation indicates an
importance of taking account of finite $N_S$ in studying open quantum systems
which may include an arbitrary number of particles in general. | cond-mat_stat-mech |
Estimating differential entropy using recursive copula splitting: A method for estimating the Shannon differential entropy of multidimensional
random variables using independent samples is described. The method is based on
decomposing the distribution into a product of the marginal distributions and
the joint dependency, also known as the copula. The entropy of marginals is
estimated using one-dimensional methods. The entropy of the copula, which
always has a compact support, is estimated recursively by splitting the data
along statistically dependent dimensions. Numerical examples demonstrate that
the method is accurate for distributions with compact and non-compact supports,
which is imperative when the support is not known or of mixed type (in
different dimensions). At high dimensions (larger than 20), our method is not
only more accurate, but also significantly more efficient than existing
approaches. | cond-mat_stat-mech |
Dynamical density functional theory for circle swimmers: The majority of studies on self-propelled particles and microswimmers
concentrates on objects that do not feature a deterministic bending of their
trajectory. However, perfect axial symmetry is hardly found in reality, and
shape-asymmetric active microswimmers tend to show a persistent curvature of
their trajectories. Consequently, we here present a particle-scale statistical
approach of circle-swimmer suspensions in terms of a dynamical density
functional theory. It is based on a minimal microswimmer model and,
particularly, includes hydrodynamic interactions between the swimmers. After
deriving the theory, we numerically investigate a planar example situation of
confining the swimmers in a circularly symmetric potential trap. There, we find
that increasing curvature of the swimming trajectories can reverse the
qualitative effect of active drive. More precisely, with increasing curvature,
the swimmers less effectively push outwards against the confinement, but
instead form high-density patches in the center of the trap. We conclude that
the circular motion of the individual swimmers has a localizing effect, also in
the presence of hydrodynamic interactions. Parts of our results could be
confirmed experimentally, for instance, using suspensions of L-shaped circle
swimmers of different aspect ratio. | cond-mat_stat-mech |
Singular relaxation of a random walk in a box with a Metropolis Monte
Carlo dynamics: We study analytically the relaxation eigenmodes of a simple Monte Carlo
algorithm, corresponding to a particle in a box which moves by uniform random
jumps. Moves outside of the box are rejected. At long times, the system
approaches the equilibrium probability density, which is uniform inside the
box. We show that the relaxation towards this equilibrium is unusual: for a
jump length comparable to the size of the box, the number of relaxation
eigenmodes can be surprisingly small, one or two. We provide a complete
analytic description of the transition between these two regimes. When only a
single relaxation eigenmode is present, a suitable choice of the symmetry of
the initial conditions gives a localizing decay to equilibrium. In this case,
the deviation from equilibrium concentrates at the edges of the box where the
rejection probability is maximal. Finally, in addition to the relaxation
analysis of the master equation, we also describe the full eigen-spectrum of
the master equation including its sub-leading eigen-modes. | cond-mat_stat-mech |
Critical behaviour of annihilating random walk of two species with
exclusion in one dimension: The $A+A\to 0$, $B+B\to 0 $ process with exclusion between the different
kinds is investigated here numerically. Before treating this model explicitly,
we study the generalized Domany-Kinzel cellular automaton model of Hinrichsen
on the line of the parameter space where only compact clusters can grow. The
simplest version is treated with two absorbing phases in addition to the active
one. The two kinds of kinks which arise in this case do not react, leading to
kinetics differing from standard annihilating random walk of two species. Time
dependent simulations are presented here to illustrate the differences caused
by exclusion in the scaling properties of usually discussed characteristic
quantities. The dependence on the density and composition of the initial state
is most apparent. Making use of the parallelism between this process and
directed percolation limited by a reflecting parabolic surface we argue that
the two kinds of kinks exert marginal perturbation on each other leading to
deviations from standard annihilating random walk behavior. | cond-mat_stat-mech |
Ashkin-Teller phase transition and multicritical behavior in a classical
monomer-dimer model: We use Monte Carlo simulations and tensor network methods to study a
classical monomer-dimer model on the square lattice with a hole (monomer)
fugacity $z$, an aligning dimer-dimer interaction $u$ that favors columnar
order, and an attractive dimer-dimer interaction $v$ between two adjacent
dimers that lie on the same principal axis of the lattice. The Monte Carlo
simulations of finite size systems rely on our grand-canonical generalization
of the dimer worm algorithm, while the tensor network computations are based on
a uniform matrix product ansatz for the eigenvector of the row-to-row transfer
matrix that work directly in the thermodynamic limit. The phase diagram has
nematic, columnar order and fluid phases, and a nonzero temperature
multicritical point at which all three meet. For any fixed $v/u < \infty$, we
argue that this multicritical point continues to be located at a nonzero hole
fugacity $z_{\rm mc}(v/u) > 0$; our numerical results confirm this theoretical
expectation but find that $z_{\rm mc}(v/u) \to 0$ very rapidly as $v/u \to
\infty$. Our numerical results also confirm the theoretical expectation that
the corresponding multicritical behavior is in the universality class of the
four-state Potts multicritical point on critical line of the two-dimensional
Ashkin-Teller model. | cond-mat_stat-mech |
Magnetization plateaus and phase diagrams of the extended Ising model on
the Shastry-Sutherland lattice: Effects of long-range interactions: Magnetization plateaus and phase diagrams of the extended Ising model on the
Shastry-Sutherland lattice with the first $(J_1)$, second $(J_2)$, third
$(J_3)$ fourth $(J_4)$ and fifth $(J_5)$ nearest-neighbour spin couplings are
studied by the classical Monte Carlo method. It is shown that switching on
$J_4$ and $J_5$ interactions (in addition to usually considered $J_1, J_2$ and
$J_3$ interactions) changes significantly the picture of magnetization
processes found for $J_4=J_5=0$ and leads to stabilization of new macroscopic
magnetic phases (plateaus) with fractional magnetization. In particular, it is
found that combined effects of $J_4$ and $J_5$ interactions generate the
following sequence of plateaus with the fractional magnetization: $m/m_s$=1/9,
1/6, 2/9, 1/3, 4/9, 1/2, 5/9 and 2/3. The results obtained are consistent with
experimental measurements of magnetization curves in selected rare-earth
tetraborides. | cond-mat_stat-mech |
Scaling Theories of Kosterlitz-Thouless Phase Transitions: We propose scaling theories for Kosterlitz-Thouless (KT) phase transitions on
the basis of the hallmark exponential growth of their correlation length.
Finite-size scaling, finite-entanglement scaling, short-time critical dynamics,
and finite-time scaling, as well as some of their combinations are studied.
Relaxation times of both a usual power-law and an unusual power-law with a
logarithmic factor are considered. Finite-size and finite-entanglement scaling
forms somehow similar to a frequently employed ansatz are presented. The
Kibble-Zurek scaling of topological defect density for a linear driving across
the KT transition point is investigated in detail. An implicit equation for a
rate exponent in the theory is derived and the exponent varies with the
distance from the critical point and the driving rate consistent with relevant
experiments. To verify the theories, we utilize the KT phase transition of a
one-dimensional Bose-Hubbard model. The infinite time-evolving-block-decimation
algorithm is employed to solve numerically the model for finite bond
dimensions. Both a correlation length and an entanglement entropy in imaginary
time and only the entanglement entropy in real-time driving are computed. Both
the short-time critical dynamics in imaginary time and the finite-time scaling
in real-time driving, both including the finite bond dimension, for the
measured quantities are found to describe the numerical results quite well via
surface collapses. The critical point is also estimated and confirmed to be
$0.302(1)$ at the infinite bond dimension on the basis of the scaling form. | cond-mat_stat-mech |
Numerical Study of the Thermodynamic Uncertainty Relation for the
KPZ-Equation: A general framework for the field-theoretic thermodynamic uncertainty
relation was recently proposed and illustrated with the $(1+1)$ dimensional
Kardar-Parisi-Zhang equation. In the present paper, the analytical results
obtained there in the weak coupling limit are tested via a direct numerical
simulation of the KPZ equation with good agreement. The accuracy of the
numerical results varies with the respective choice of discretization of the
KPZ non-linearity. Whereas the numerical simulations strongly support the
analytical predictions, an inherent limitation to the accuracy of the
approximation to the total entropy production is found. In an analytical
treatment of a generalized discretization of the KPZ non-linearity, the origin
of this limitation is explained and shown to be an intrinsic property of the
employed discretization scheme. | cond-mat_stat-mech |
On the von Neumann entropy of a bath linearly coupled to a driven
quantum system: The change of the von Neumann entropy of a set of harmonic oscillators
initially in thermal equilibrium and interacting linearly with an externally
driven quantum system is computed by adapting the Feynman-Vernon influence
functional formalism. This quantum entropy production has the form of the
expectation value of three functionals of the forward and backward paths
describing the system history in the Feynman-Vernon theory. In the classical
limit of Kramers-Langevin dynamics (Caldeira-Leggett model) these functionals
combine to three terms, where the first is the entropy production functional of
stochastic thermodynamics, the classical work done by the system on the
environment in units of $k_BT$, the second another functional with no analogue
in stochastic thermodynamics, and the third is a boundary term. | cond-mat_stat-mech |
Pipe network model for scaling of dynamic interfaces in porous media: We present a numerical study on the dynamics of imbibition fronts in porous
media using a pipe network model. This model quantitatively reproduces the
anomalous scaling behavior found in imbibition experiments [Phys. Rev. E {\bf
52}, 5166 (1995)]. Using simple scaling arguments, we derive a new identity
among the scaling exponents in agreement with the experimental results. | cond-mat_stat-mech |
Communication and optimal hierarchical networks: We study a general and simple model for communication processes. In the
model, agents in a network (in particular, an organization) interchange
information packets following simple rules that take into account the limited
capability of the agents to deal with packets and the cost associated to the
existence of open communication channels. Due to the limitation in the
capability, the network collapses under certain conditions. We focus on when
the collapse occurs for hierarchical networks and also on the influence of the
flatness or steepness of the structure. We find that the need for hierarchy is
related to the existence of costly connections. | cond-mat_stat-mech |
Radial marginal perturbation of two-dimensional systems and conformal
invariance: The conformal mapping w=(L/2\pi)\ln z transforms the critical plane with a
radial perturbation \alpha\rho^{-y} into a cylinder with width L and a constant
deviation \alpha(2\pi/L)^y from the bulk critical point when the decay exponent
y is such that the perturbation is marginal. From the known behavior of the
homogeneous off-critical system on the cylinder, one may deduce the correlation
functions and defect exponents on the perturbed plane. The results are
supported by an exact solution for the Gaussian model. | cond-mat_stat-mech |
Jamming and Stress Propagation in Particulate Matter: We present simple models of particulate materials whose mechanical integrity
arises from a jamming process. We argue that such media are generically
"fragile", that is, they are unable to support certain types of incremental
loading without plastic rearrangement. In such models, fragility is naturally
linked to the marginal stability of force chain networks (granular skeletons)
within the material. Fragile matter exhibits novel mechanical responses that
may be relevant to both jammed colloids and cohesionless assemblies of poured,
rigid grains. | cond-mat_stat-mech |
A non perturbative approach of the principal chiral model between two
and four dimensions: We investigate the principal chiral model between two and four dimensions by
means of a non perturbative Wilson-like renormalization group equation. We are
thus able to follow the evolution of the effective coupling constants within
this whole range of dimensions without having recourse to any kind of small
parameter expansion. This allows us to identify its three dimensional critical
physics and to solve the long-standing discrepancy between the different
perturbative approaches that characterizes the class of models to which the
principal chiral model belongs. | cond-mat_stat-mech |
Macroscopically measurable force induced by temperature discontinuities
at solid-gas interfaces: We consider a freely movable solid that separates a long tube into two
regions, each of which is filled with a dilute gas. The gases in each region
are initially prepared at the same pressure but different temperatures. Under
the assumption that the pressure and temperatures of gas particles before
colliding with the solid are kept constant over time, we show that temperature
gaps appearing on the solid surface generate a force. We provide a quantitative
estimation of the force, which turns out to be large enough to be observed by a
macroscopic measurement. | cond-mat_stat-mech |
Burr, Levy, Tsallis: The purpose of this short paper dedicated to the 60th anniversary of
Prof.Constantin Tsallis is to show how the use of mathematical tools and
physical concepts introduced by Burr, L\.{e}vy and Tsallis open a new line of
analysis of the old problem of non-Debye decay and universality of relaxation.
We also show how a finite characteristic time scale can be expressed in terms
of a $q$-expectation using the concept of $q$- escort probability.The
comparison with the Weron et al. probabilistic theory of relaxation leads to a
better understanding of the stochastic properties underlying the Tsallis
entropy concept. | cond-mat_stat-mech |
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY
Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of
Hierarchical Models: Hierarchical lattices that constitute spatially anisotropic systems are
introduced. These lattices provide exact solutions for hierarchical models and,
simultaneously, approximate solutions for uniaxially or fully anisotropic d=3
physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers,
are obtained for Ising, XY magnetic models and percolation systems, including
crossovers from algebraic order to true long-range order. | cond-mat_stat-mech |
Relativistic antifragility: It is shown that the barbell distribution of a gas of relativistic molecules
above its critical temperature, can be interpreted as an antifragile response
to the relativistic constraint of subluminal propagation. | cond-mat_stat-mech |
Generalized arcsine laws for fractional Brownian motion: The three arcsine laws for Brownian motion are a cornerstone of extreme-value
statistics. For a Brownian $B_t$ starting from the origin, and evolving during
time $T$, one considers the following three observables: (i) the duration $t_+$
the process is positive, (ii) the time $t_{\rm last}$ the process last visits
the origin, and (iii) the time $t_{\rm max}$ when it achieves its maximum (or
minimum). All three observables have the same cumulative probability
distribution expressed as an arcsine function, thus the name of arcsine laws.
We show how these laws change for fractional Brownian motion $X_t$, a
non-Markovian Gaussian process indexed by the Hurst exponent $H$. It
generalizes standard Brownian motion (i.e. $H=\tfrac{1}{2}$). We obtain the
three probabilities using a perturbative expansion in $\epsilon =
H-\tfrac{1}{2}$. While all three probabilities are different, this distinction
can only be made at second order in $\epsilon$. Our results are confirmed to
high precision by extensive numerical simulations. | cond-mat_stat-mech |
Symmetry and species segregation in diffusion-limited pair annihilation: We consider a system of q diffusing particle species A_1,A_2,...,A_q that are
all equivalent under a symmetry operation. Pairs of particles may annihilate
according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the
symmetry, and without self-annihilation (k_{ii} = 0). In spatial dimensions d >
2 mean-field theory predicts that the total particle density decays as n(t) ~
1/t, provided the system remains spatially uniform. We determine the conditions
on the matrix k under which there exists a critical segregation dimension
d_{seg} below which this uniformity condition is violated; the symmetry between
the species is then locally broken. We argue that in those cases the density
decay slows down to n(t) ~ t^{-d/d_{seg}} for 2 < d < d_{seg}. We show that
when d_{seg} exists, its value can be expressed in terms of the ratio of the
smallest to the largest eigenvalue of k. The existence of a conservation law
(as in the special two-species annihilation A + B -> 0), although sufficient
for segregation, is shown not to be a necessary condition for this phenomenon
to occur. We work out specific examples and present Monte Carlo simulations
compatible with our analytical results. | cond-mat_stat-mech |
Effects of turbulent mixing on critical behaviour: Renormalization group
analysis of the Potts model: Critical behaviour of a system, subjected to strongly anisotropic turbulent
mixing, is studied by means of the field theoretic renormalization group.
Specifically, relaxational stochastic dynamics of a non-conserved
multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a
random velocity field with prescribed statistics, is considered. The velocity
is taken Gaussian, white in time, with correlation function of the form
$\propto \delta(t-t') /|{\bf k}_{\bot}|^{d-1+\xi}$, where ${\bf k}_{\bot}$ is
the component of the wave vector, perpendicular to the distinguished direction
("direction of the flow") --- the $d$-dimensional generalization of the
ensemble introduced by Avellaneda and Majda [1990 {\it Commun. Math. Phys.}
{\bf 131} 381] within the context of passive scalar advection. This model can
describe a rich class of physical situations. It is shown that, depending on
the values of parameters that define self-interaction of the order parameter
and the relation between the exponent $\xi$ and the space dimension $d$, the
system exhibits various types of large-scale scaling behaviour, associated with
different infrared attractive fixed points of the renormalization-group
equations. In addition to known asymptotic regimes (critical dynamics of the
Potts model and passively advected field without self-interaction), existence
of a new, non-equilibrium and strongly anisotropic, type of critical behaviour
(universality class) is established, and the corresponding critical dimensions
are calculated to the leading order of the double expansion in $\xi$ and
$\epsilon=6-d$ (one-loop approximation). The scaling appears strongly
anisotropic in the sense that the critical dimensions related to the directions
parallel and perpendicular to the flow are essentially different. | cond-mat_stat-mech |
One-dimensional fluids with positive potentials: We study a class of one-dimensional classical fluids with penetrable
particles interacting through positive, purely repulsive, pair-potentials.
Starting from some lower bounds to the total potential energy, we draw results
on the thermodynamic limit of the given model. | cond-mat_stat-mech |
Reply to Comment on `Monte-Carlo simulation study of the two-stage
percolation transition in enhanced binary trees': We discuss the nature of the two-stage percolation transition on the enhanced
binary tree in order to explain the disagreement in the estimation of the
second transition probability between the one in our recent paper (J. Phys.
A:Math. Theor. 42 (2009) 145001) and the one in the comment to it from Baek,
Minnhagen and Kim. We point out some reasons that the finite size scaling
analysis used by them is not proper for the enhanced tree due to its
nonamenable nature, which is verified by some numerical results. | cond-mat_stat-mech |
Comments on Generalization of thermodynamics in of fractional-order
derivatives and calculation of heat transfer properties of noble gases,
Journal of Thermal Analysis and Calorimetry 2018 133, 1189 1194: It is shown that the equations for pressure, entropy and the isochoric heat
capacity obtained by using generalization of the equilibrium thermodynamics in
fractional derivatives in the paper mentioned above are approximate, the
comparison of the equations with the experimental (tabulated) data for Neon and
Argon made in the paper is incorrect, and the conclusions of the paper made on
the basis of the comparison could be incorrect. The conditions for validity of
the equations are established. It is also established that the question about a
physical sense of the exponent of the derivative of a fractional order is still
open. | cond-mat_stat-mech |
Attractive energy and entropy or particle size: the yin and yang of
physical and biological science: It is well known that equilibrium in a thermodynamic system results from a
competition or balance between lowering the energy and increasing the entropy,
or at least the product of the temperature and entropy. This is remarkably
similar to the Taoist concept of yin, a downward influence, and yang, an upward
influence, where harmony is established by balancing yin and yang. Entropy is
due to structure, which is largely determined by core repulsions or particle
size whereas energy is largely determined by longer range attractive
interactions. Here, this balance between energy and entropy or particle size is
traced through the theory of simple fluids, beginning with Andrews and van der
Waals, the subsequent developments of perturbation theory, theories of
correlation functions that are based on the Ornstein-Zernike relation and the
mean spherical approximation, electrolytes, and recent work on ion channels in
biological membranes, where the competition between energy and size gives an
intuitively attractive explanation of the selectivity of cation channels.
Simulations of complex systems, including proteins in aqueous solution, should
be studied to determine the extent to which these concepts are useful for such
situations | cond-mat_stat-mech |
Percolation on a Feynman Diagram: In a recent paper hep-lat/9704020 we investigated Potts models on ``thin''
random graphs -- generic Feynman diagrams, using the idea that such models may
be expressed as the N --> 1 limit of a matrix model. The models displayed first
order transitions for all q greater than 2, giving identical behaviour to the
corresponding Bethe lattice.
We use here one of the results of hep-lat/9704020 namely a general saddle
point solution for a q state Potts model expressed as a function of q, to
investigate some peculiar features of the percolative limit q -> 1 and compare
the results with those on the Bethe lattice. | cond-mat_stat-mech |
Second-order phase transition in the Heisenberg model on a triangular
lattice with competing interactions: We discover an example where the dissociation of the Z2 vortices occurs at
the second-order phase transition point. We investigate the nature of phase
transition in a classical Heisenberg model on a distorted triangular lattice
with competing interactions. The order parameter space of the model is
SO(3)xZ2. The dissociation of the Z2 vortices which comes from SO(3) and a
second-order phase transition with Z2 symmetry breaking occur at the same
temperature. We also find that the second-order phase transition belongs to the
universality class of the two-dimensional Ising model. | cond-mat_stat-mech |
Linear response subordination to intermittent energy release in
off-equilibrium aging dynamics: The interpretation of experimental and numerical data describing
off-equilibrium aging dynamics crucially depends on the connection between
spontaneous and induced fluctuations. The hypothesis that linear response
fluctuations are statistically subordinated to irreversible outbursts of
energy, so-called quakes, leads to predictions for averages and fluctuations
spectra of physical observables in reasonable agreement with experimental
results [see e.g. Sibani et al., Phys. Rev. B74:224407, 2006]. Using
simulational data from a simple but representative Ising model with plaquette
interactions, direct statistical evidence supporting the hypothesis is
presented and discussed in this work.
A strict temporal correlation between quakes and intermittent magnetization
fluctuations is demonstrated. The external magnetic field is shown to bias the
pre-existent intermittent tails of the magnetic fluctuation distribution, with
little or no effect on the Gaussian part of the latter. Its impact on energy
fluctuations is shown to be negligible.
Linear response is thus controlled by the quakes and inherits their temporal
statistics. These findings provide a theoretical basis for analyzing
intermittent linear response data from aging system in the same way as thermal
energy fluctuations, which are far more difficult to measure. | cond-mat_stat-mech |
Some general features of matrix product states in stochastic systems: We will prove certain general relations in Matrix Product Ansatz for one
dimensional stochastic systems, which are true in both random and sequential
updates. We will derive general MPA expressions for the currents and current
correlators and find the conditions in the MPA formalism, under which the
correlators are site-independent or completely vanishing. | cond-mat_stat-mech |
Effects of turbulent mixing on the nonequilibrium critical behaviour: We study effects of turbulent mixing on the critical behaviour of a
nonequilibrium system near its second-order phase transition between the
absorbing and fluctuating states. The model describes the spreading of an agent
(e.g., infectious disease) in a reaction-diffusion system and belongs to the
universality class of the directed bond percolation process, also known as
simple epidemic process, and is equivalent to the Reggeon field theory. The
turbulent advecting velocity field is modelled by the Obukhov--Kraichnan's
rapid-change ensemble: Gaussian statistics with the correlation function < vv>
\propto \delta(t-t') k^{-d-\xi}, where k is the wave number and 0<\xi<2 is a
free parameter. Using the field theoretic renormalization group we show that,
depending on the relation between the exponent \xi and the space dimensionality
d, the system reveals different types of large-scale asymptotic behaviour,
associated with four possible fixed points of the renormalization group
equations. In addition to known regimes (ordinary diffusion, ordinary directed
percolation process, and passively advected scalar field), existence of a new
nonequilibrium universality class is established, and the corresponding
critical dimensions are calculated to first order of the double expansion in
\xi and \varepsilon=4-d (one-loop approximation). It turns out, however, that
the most realistic values \xi=4/3 (Kolmogorov's fully developed turbulence) and
d=2 or 3 correspond to the case of passive scalar field, when the nonlinearity
of the Reggeon model is irrelevant and the spreading of the agent is completely
determined by the turbulent transfer. | cond-mat_stat-mech |
Wet Sand flows better than dry sand: We investigated the yield stress and the apparent viscosity of sand with and
without small amounts of liquid. By pushing the sand through a tube with an
enforced Poiseuille like profile we minimize the effect of avalanches and shear
localization. We find that the system starts to flow when a critical shear of
the order of one particle diameter is exceeded. In contrast to common believe,
we observe that the resistance against the flow of wet sand is much smaller
than that of dry sand. For the dissipative flow we propose a non-equilibrium
state equation for granular fluids. | cond-mat_stat-mech |
Characterization of Sleep Stages by Correlations of Heartbeat Increments: We study correlation properties of the magnitude and the sign of the
increments in the time intervals between successive heartbeats during light
sleep, deep sleep, and REM sleep using the detrended fluctuation analysis
method. We find short-range anticorrelations in the sign time series, which are
strong during deep sleep, weaker during light sleep and even weaker during REM
sleep. In contrast, we find long-range positive correlations in the magnitude
time series, which are strong during REM sleep and weaker during light sleep.
We observe uncorrelated behavior for the magnitude during deep sleep. Since the
magnitude series relates to the nonlinear properties of the original time
series, while the signs series relates to the linear properties, our findings
suggest that the nonlinear properties of the heartbeat dynamics are more
pronounced during REM sleep. Thus, the sign and the magnitude series provide
information which is useful in distinguishing between the sleep stages. | cond-mat_stat-mech |
Frequency clustering and disaggregation in idealized fractal tree: The pattern of formation of resonant frequency clusters in idealized
sympodial dichasium trees is revealed by numerical modeling and analysis. The
larger cluster's cardinality correlates with that of a Small World Network,
which share the same adjacency matrix. Topology and inherent symmetry of the
structure dictate compartmentalization of the modal characteristics and
robustness to perturbations to the limb geometry, and are not limited to a
specific allometry. When the spatial symmetry of the limb geometry is perturbed
above a certain level, we see percolation of the largest cluster. | cond-mat_stat-mech |
Wind on the boundary for the Abelian sandpile model: We continue our investigation of the two-dimensional Abelian sandpile model
in terms of a logarithmic conformal field theory with central charge c=-2, by
introducing two new boundary conditions. These have two unusual features: they
carry an intrinsic orientation, and, more strangely, they cannot be imposed
uniformly on a whole boundary (like the edge of a cylinder). They lead to seven
new boundary condition changing fields, some of them being in highest weight
representations (weights -1/8, 0 and 3/8), some others belonging to
indecomposable representations with rank 2 Jordan cells (lowest weights 0 and
1). Their fusion algebra appears to be in full agreement with the fusion rules
conjectured by Gaberdiel and Kausch. | cond-mat_stat-mech |
Low-temperature behavior of the $O(N)$ models below two dimensions: We investigate the critical behavior and the nature of the low-temperature
phase of the $O(N)$ models treating the number of field components $N$ and the
dimension $d$ as continuous variables with a focus on the $d\leq 2$ and $N\leq
2$ quadrant of the $(d,N)$ plane. We precisely chart a region of the $(d,N)$
plane where the low-temperature phase is characterized by an algebraic
correlation function decay similar to that of the Kosterlitz-Thouless phase but
with a temperature-independent anomalous dimension $\eta$. We revisit the
Cardy-Hamber analysis leading to a prediction concerning the nonanalytic
behavior of the $O(N)$ models' critical exponents and emphasize the previously
not broadly appreciated consequences of this approach in $d<2$. In particular,
we discuss how this framework leads to destabilization of the long-range order
in favour of the quasi long-range order in systems with $d<2$ and $N<2$.
Subsequently, within a scheme of the nonperturbative renormalization group we
identify the low-temperature fixed points controlling the quasi long-range
ordered phase and demonstrate a collision between the critical and the
low-temperature fixed points upon approaching the lower critical dimension. We
evaluate the critical exponents $\eta(d,N)$ and $\nu^{-1}(d,N)$ and demonstrate
a very good agreement between the predictions of the Cardy-Hamber type analysis
and the nonperturbative renormalization group in $d<2$. | cond-mat_stat-mech |
From the density functional to the single-particle Green function: An analysis shows that the ground state of the inhomogeneous system of
interacting electrons in the static external field, which satisfies the
thermodynamic limit, can be consistently described only using the Green
function theory based on the quantum field theory methods (perturbation theory
diagram technique). In this case, the ground state energy and inhomogeneous
electron density in such a system can be determined only after calculating the
single-particle Green function. | cond-mat_stat-mech |
A Biologically Motivated Asymmetric Exclusion Process: interplay of
congestion in RNA polymerase traffic and slippage of nascent transcript: We develope a theoretical framework, based on exclusion process, that is
motivated by a biological phenomenon called transcript slippage (TS). In this
model a discrete lattice represents a DNA strand while each of the particles
that hop on it unidirectionally, from site to site, represents a RNA polymerase
(RNAP). While walking like a molecular motor along a DNA track in a
step-by-step manner, a RNAP simultaneously synthesizes a RNA chain; in each
forward step it elongates the nascent RNA molecule by one unit, using the DNA
track also as the template. At some special "slippery" position on the DNA,
which we represent as a defect on the lattice, a RNAP can lose its grip on the
nascent RNA and the latter's consequent slippage results in a final product
that is either longer or shorter than the corresponding DNA template. We
develope an exclusion model for RNAP traffic where the kinetics of the system
at the defect site captures key features of TS events. We demonstrate the
interplay of the crowding of RNAPs and TS. A RNAP has to wait at the defect
site for longer period in a more congested RNAP traffic, thereby increasing the
likelihood of its suffering a larger number of TS events. The qualitative
trends of some of our results for a simple special case of our model are
consistent with experimental observations. The general theoretical framework
presented here will be useful for guiding future experimental queries and for
analysis of the experimental data with more detailed versions of the same
model. | cond-mat_stat-mech |
50 years of correlations with Michael Fisher and the renormalization
group: This paper will be published in ``50 years of the renormalization group",
dedicated to the memory of Michael E. Fisher, edited by Amnon Aharony, Ora
Entin-Wohlman, David Huse, and Leo Radzihovsky, World Scientific. I start with
a review of my personal and scientific interactions with Michael E. Fisher, who
was my post-doc mentor in 1972-1974. I then describe several recent
renormalization group studies, which started during those years, and still
raise some open issues. These include the magnets with dipole-dipole
interactions, the puzzle of the bicritical points and the random field Ising
model. | cond-mat_stat-mech |
Nonergodic Brownian oscillator: Low-frequency response: An undisturbed Brownian oscillator may not reach thermal equilibrium with the
thermal bath due to the formation of a localized normal mode. The latter may
emerge when the spectrum of the thermal bath has a finite upper bound
$\omega_0$ and the oscillator natural frequency exceeds a critical value
$\omega_c$, which depends on the specific form of the bath spectrum. We
consider the response of the oscillator with and without a localized mode to
the external periodic force with frequency $\Omega$ lower than $\omega_0$. The
results complement those obtained earlier for the high-frequency response at
$\Omega\ge \omega_0$ and require a different mathematical approach. The
signature property of the high-frequency response is resonance when the
external force frequency $\Omega$ coincides with the frequency of the localized
mode $\omega_*$. In the low-frequency domain $\Omega<\omega_0$ the condition of
resonance $\Omega=\omega_*$ cannot be met (since $\omega_*>\omega_0$). Yet, in
the limits $\omega\to\omega_c$ and $\Omega\to\omega_0^-$, the oscillator shows
a peculiar quasi-resonance response with an amplitude increasing with time
sublinearly. | cond-mat_stat-mech |
Fluctuations and Criticality of a Granular Solid-Liquid-like Phase
Transition: We present an experimental study of density and order fluctuations in the
vicinity of the solid-liquid-like transition that occurs in a vibrated
quasi-two-dimensional granular system. The two-dimensional projected static and
dynamic correlation functions are studied. We show that density fluctuations,
characterized through the structure factor, increase in size and intensity as
the transition is approached, but they do not change significantly at the
transition itself. The dense, metastable clusters, which present square
symmetry, also increase their local order in the vicinity of the transition.
This is characterized through the bond-orientational order parameter $Q_4$,
which in Fourier space obeys an Ornstein-Zernike behavior. Depending on filling
density and vertical height, the transition can be of first or second order
type. In the latter case, the associated correlation length $\xi_4$, relaxation
time $\tau_4$, zero $k$ limit of $Q_4$ fluctuations (static susceptibility),
the pair correlation function of $Q_4$, and the amplitude of the order
parameter obey critical power laws, with saturations due to finite size
effects. Their respective critical exponents are $\nu_{\bot} = 1$, $\nu_{||} =
2$, $\gamma = 1$, $\eta=0.67$, and $\beta=1/2$, whereas the dynamical critical
exponent $z = \nu_{||}/\nu_{\bot} = 2$. These results are consistent with model
C of dynamical critical phenomena, valid for a non-conserved critical order
parameter (bond-orientation order) coupled to a conserved field (density). | cond-mat_stat-mech |
Nonequilibrium thermodynamics as a gauge theory: We assume that markovian dynamics on a finite graph enjoys a gauge symmetry
under local scalings of the probability density, derive the transformation law
for the transition rates and interpret the thermodynamic force as a gauge
potential. A widely accepted expression for the total entropy production of a
system arises as the simplest gauge-invariant completion of the time derivative
of Gibbs's entropy. We show that transition rates can be given a simple
physical characterization in terms of locally-detailed-balanced heat
reservoirs. It follows that Clausius's measure of irreversibility along a
cyclic transformation is a geometric phase. In this picture, the gauge symmetry
arises as the arbitrariness in the choice of a prior probability. Thermostatics
depends on the information that is disposable to an observer; thermodynamics
does not. | cond-mat_stat-mech |
Gauge Invariant Formulations of Dicke-Preparata Super-Radiant Models: In a gauge invariant formulation of the molecular electric dipole-photon
interaction, the rigorous coupling is strictly linear in the photon creation
and photon annihilation operators. The linear coupling allows for a
super-radiant phase transition as in the Hepp-Lieb formulation. A previous
notion of a quadratic-coupling ``no-go theorem'' for super-radiance is
incorrect. Also incorrect is a previous assertion that the dipole-photon
coupling has absolutely no effect on the thermal equations of state. These
dubious assertions were based on incorrect canonical transformations which
eliminated the electric field (and thereby eliminated the dipole-photon
interaction) which is neither mathematically nor physically consistent. The
correct form of the canonical transformations are given in this work which
allows for the physical reality of super-radiant condensed matter phases. | cond-mat_stat-mech |
Aging and fluctuation-dissipation ratio for the diluted Ising Model: We consider the out-of-equilibrium, purely relaxational dynamics of a weakly
diluted Ising model in the aging regime at criticality. We derive at first
order in a $\sqrt{\epsilon}$ expansion the two-time response and correlation
functions for vanishing momenta. The long-time limit of the critical
fluctuation-dissipation ratio is computed at the same order in perturbation
theory. | cond-mat_stat-mech |
Organic nanowires and chiral patterns of tetracyanoquinodimethane (TCNQ)
grown by vacuum vapor deposition: Organic nanowires and quasi-two-dimensional chiral patterns of
tetracyanoquinodimethane have been successfully generated by vacuum thermal
evaporation. The nanowires and patterns were characterized by using atomic
force microscopy and transmission electron microscopy. The influence of
electric charged clusters, deposition rate, and substrate temperature were
experimentally investigated. Contrary to previous reports, charged clusters are
found to be unnecessary to the chiral pattern formation. It was shown that the
nanowire and pattern formation should be mainly dominated by its special
crystallization properties, though the effect of the growth conditions cannot
be neglected. | cond-mat_stat-mech |
Survival Analysis, Master Equation, Efficient Simulation of Path-Related
Quantities, and Hidden State Concept of Transitions: This paper presents and derives the interrelations between survival analysis
and master equation. Survival analysis deals with modeling the transitions
between succeeding states of a system in terms of hazard rates. Questions
related with this are the timing and sequencing of the states of a time series.
The frequency and characteristics of time series can be investigated by
Monte-Carlo simulations. If one is interested in cross-sectional data connected
with the stochastic process under consideration, one needs to know the temporal
evolution of the distribution of states. This can be obtained by simulation of
the associated master equation. Some new formulas allow the determination of
path-related (i.e. longitudinal) quantities like the occurence probability, the
occurence time distribution, or the effective cumulative life-time distribution
of a certain sequencing of states (path). These can be efficiently evaluated
with a recently developed simulation tool (EPIS). The effective cumulative
life-time distribution facilitates the formulation of a hidden state concept of
behavioral changes which allows an interpretation of the respective
time-dependence of hazard rates. Hidden states represent states which are
either not phenomenological distinguishable from other states, not externally
measurable, or simply not detected. | cond-mat_stat-mech |
Analytical calculations of the Quantum Tsallis thermodynamic variables: In this article, we provide an account of analytical results related to the
Tsallis thermodynamics that have been the subject matter of a lot of studies in
the field of high-energy collisions. After reviewing the results for the
classical case in the massless limit and for arbitrarily massive classical
particles, we compute the quantum thermodynamic variables. For the first time,
the analytical formula for the pressure of a Tsallis-like gas of massive bosons
has been obtained. Hence, this article serves both as a brief review of the
knowledge gathered in this area, and as an original research that forwards the
existing scholarship. The results of the present paper will be important in a
plethora of studies in the field of high-energy collisions including the
propagation of non-linear waves generated by the traversal of high-energy
particles inside the quark-gluon plasma medium showing the features of
non-extensivity. | cond-mat_stat-mech |
Coagulation kinetics beyond mean field theory using an optimised Poisson
representation: Binary particle coagulation can be modelled as the repeated random process of
the combination of two particles to form a third. The kinetics can be
represented by population rate equations based on a mean field assumption,
according to which the rate of aggregation is taken to be proportional to the
product of the mean populations of the two participants. This can be a poor
approximation when the mean populations are small. However, using the Poisson
representation it is possible to derive a set of rate equations that go beyond
mean field theory, describing pseudo-populations that are continuous, noisy and
complex, but where averaging over the noise and initial conditions gives the
mean of the physical population. Such an approach is explored for the simple
case of a size-independent rate of coagulation between particles. Analytical
results are compared with numerical computations and with results derived by
other means. In the numerical work we encounter instabilities that can be
eliminated using a suitable 'gauge' transformation of the problem [P. D.
Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the
application of the Cameron-Martin-Girsanov formula describing a shift in a
probability measure. The cost of such a procedure is to introduce additional
statistical noise into the numerical results, but we identify an optimised
gauge transformation where this difficulty is minimal for the main properties
of interest. For more complicated systems, such an approach is likely to be
computationally cheaper than Monte Carlo simulation. | cond-mat_stat-mech |
Universal free energy correction for the two-dimensional one-component
plasma: The universal finite-size correction to the free energy of a two-dimensional
Coulomb system is checked in the special case of a one-component plasma on a
sphere. The correction is related to the known second moment of the short-range
part of the direct correlation function for a planar system. | cond-mat_stat-mech |
Eliminating the cuspidal temperature profile of a non-equilibrium chain: In 1967, Z. Rieder, J. L. Lebowitz and E. Lieb (RLL) introduced a model of
heat conduction on a crystal that became a milestone problem of non-equilibrium
statistical mechanics. Along with its inability to reproduce Fourier's Law -
which subsequent generalizations have been trying to amend - the RLL model is
also characterized by awkward cusps at the ends of the non-equilibrium chain,
an effect that has endured all these years without a satisfactory answer. In
this paper, we first show that such trait stems from the insufficiency of
pinning interactions between the chain and the substrate. Assuming the
possibility of pinning the chain, the analysis of the temperature profile in
the space of parameters reveals that for a proper combination of the border and
bulk pinning values, the temperature profile may shift twice between the RLL
cuspidal behavior and the expected monotonic local temperature evolution along
the system, as a function of the pinning. At those inversions, the temperature
profile along the chain is characterized by perfect plateaux: at the first
threshold, the cumulants of the heat flux reach their maxima and the vanishing
of the two-point velocity correlation function for all sites of the chain so
that the system behaves similarly to a "phonon box". On the other hand, at the
second change of the temperature profile, we still have the vanishing of the
two-point correlation function but only for the bulk, which explains the
emergence of the temperature plateau and thwarts the reaching of the maximal
values of the cumulants of the heat flux. | cond-mat_stat-mech |
Evolutionary design of non-frustrated networks of phase-repulsive
oscillators: Evolutionary optimisation algorithm is employed to design networks of
phase-repulsive oscillators that achieve an anti-phase synchronised state. By
introducing the link frustration, the evolutionary process is implemented by
rewiring the links with probability proportional to their frustration, until
the final network displaying a unique non-frustrated dynamical state is
reached. Resulting networks are bipartite and with zero clustering. In
addition, the designed non-frustrated anti-phase synchronised networks display
a clear topological scale. This contrasts usually studied cases of networks
with phase-attractive dynamics, whose performance towards full synchronisation
is typically enhanced by the presence of a topological hierarchy. | cond-mat_stat-mech |
Quasi-elastic solutions to the nonlinear Boltzmann equation for
dissipative gases: The solutions of the one-dimensional homogeneous nonlinear Boltzmann equation
are studied in the QE-limit (Quasi-Elastic; infinitesimal dissipation) by a
combination of analytical and numerical techniques. Their behavior at large
velocities differs qualitatively from that for higher dimensional systems. In
our generic model, a dissipative fluid is maintained in a non-equilibrium
steady state by a stochastic or deterministic driving force. The velocity
distribution for stochastic driving is regular and for infinitesimal
dissipation, has a stretched exponential tail, with an unusual stretching
exponent $b_{QE} = 2b$, twice as large as the standard one for the
corresponding $d$-dimensional system at finite dissipation. For deterministic
driving the behavior is more subtle and displays singularities, such as
multi-peaked velocity distribution functions. We classify the corresponding
velocity distributions according to the nature and scaling behavior of such
singularities. | cond-mat_stat-mech |
Scaling of the glassy dynamics of soft repulsive particles: a
mode-coupling approach: We combine the hyper-netted chain approximation of liquid state theory with
the mode-coupling theory of the glass transition to analyze the structure and
dynamics of soft spheres interacting via harmonic repulsion. We determine the
locus of the fluid-glass dynamic transition in a temperature -- volume fraction
phase diagram. The zero-temperature (hard sphere) glass transition influences
the dynamics at finite temperatures in its vicinity. This directly implies a
form of dynamic scaling for both the average relaxation time and dynamic
susceptibilities quantifying dynamic heterogeneity. We discuss several
qualitative disagreements between theory and existing simulations at
equilibrium. Our theoretical results are, however, very similar to numerical
results for the driven athermal dynamics of repulsive spheres, suggesting that
`mean-field' mode-coupling approaches might be good starting points to describe
these nonequilibrium dynamics. | cond-mat_stat-mech |
Low temperature ratchet current: In [3], the low temperature ratchet current in a multilevel system is
considered. In this note, we give an explicit expression for it and find its
numerical value as the number of states goes to infinity. | cond-mat_stat-mech |
Series Expansion of the Percolation Threshold on Hypercubic Lattices: We study proper lattice animals for bond- and site-percolation on the
hypercubic lattice $\mathbb{Z}^d$ to derive asymptotic series of the
percolation threshold $p_c$ in $1/d$, The first few terms of these series were
computed in the 1970s, but the series have not been extended since then. We add
two more terms to the series for $\pcsite$ and one more term to the series for
$\pcbond$, using a combination of brute-force enumeration, combinatorial
identities and an approach based on Pad\'e approximants, which requires much
fewer resources than the classical method. We discuss why it took 40 years to
compute these terms, and what it would take to compute the next ones. En
passant, we present new perimeter polynomials for site and bond percolation and
numerical values for the growth rate of bond animals. | cond-mat_stat-mech |
Statistical origin of Legendre invariant metrics: Legendre invariant metrics have been introduced in Geometrothermodynamics to
take into account the important fact that the thermodynamic properties of
physical systems do not depend on the choice of thermodynamic potential from a
geometric perspective. In this work, we show that these metrics also have a
statistical origin which can be expressed in terms of the average and variance
of the differential of the microscopic entropy. To show this, we use a
particular reparametrization of the coordinates of the corresponding
thermodynamic phase space. | cond-mat_stat-mech |
Permutation Phase and Gentile Statistics: This paper presents a new way to construct single-valued many-body
wavefunctions of identical particles with intermediate exchange phases between
Fermi and Bose statistics. It is demonstrated that the exchange phase is not a
representation character but the \textit{word metric} of the permutation group,
beyond the anyon phase from the braiding group in two dimensions. By
constructing this type of wavefunction from the direct product of
single-particle states, it is shown that a finite \textit{capacity q} -- the
maximally allowed particle occupation of each quantum state, naturally arises.
The relation between the permutation phase and capacity is given, interpolating
between fermions and bosons in the sense of both exchange phase and occupation
number. This offers a quantum mechanics foundation for \textit{Gentile
statistics} and new directions to explore intermediate statistics and anyons. | cond-mat_stat-mech |
Kinetic theory of collisionless relaxation for systems with long-range
interactions: We develop the kinetic theory of collisionless relaxation for systems with
long-range interactions in relation to the statistical theory of Lynden-Bell.
We treat the multi-level case. We make the connection between the kinetic
equation obtained from the quasilinear theory of the Vlasov equation and the
relaxation equation obtained from a maximum entropy production principle. We
propose a method to close the infinite hierarchy of kinetic equations for the
phase level moments and obtain a kinetic equation for the coarse-grained
distribution function in the form of a generalized Landau, Lenard-Balescu or
Kramers equation associated with a generalized form of entropy [P.H. Chavanis,
Physica A {\bf 332}, 89 (2004)]. This allows us to go beyond the two-level case
associated with a Fermi-Dirac-type entropy. We discuss the numerous analogies
with two-dimensional turbulence. We also mention possible applications of the
present formalism to fermionic and bosonic dark matter halos. | cond-mat_stat-mech |
Optimal protocols for Hamiltonian and Schrödinger dynamics: For systems in an externally controllable time-dependent potential, the
optimal protocol minimizes the mean work spent in a finite-time transition
between given initial and final values of a control parameter. For an initially
thermalized ensemble, we consider both Hamiltonian evolution for classical
systems and Schr\"odinger evolution for quantum systems. In both cases, we show
that for harmonic potentials, the optimal work is given by the adiabatic work
even in the limit of short transition times. This result is counter-intuitive
because the adiabatic work is substantially smaller than the work for an
instantaneous jump. We also perform numerical calculations of the optimal
protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a
two-level spin system, we give examples where the adiabatic work can be reached
in either a finite or an arbitrarily short transition time depending on the
allowed parameter space. | cond-mat_stat-mech |
Explicit formula of energy-conserving Fokker-Planck type collision term
for single species point vortex systems with weak mean flow: This paper derives a kinetic equation for a two-dimensional single species
point vortex system. We consider a situation (different from the ones
considered previously) of weak mean flow where the time scale of the
macroscopic motion is longer than the decorrelation time so that the trajectory
of the point vortices can be approximated by a straight line on the
decorrelation time scale. This may be the case when the number $N$ of point
vortices is not too large. Using a kinetic theory based on the Klimontovich
formalism, we derive a collision term consisting of a diffusion term and a
drift term, whose structure is similar to the Fokker-Planck equation. The
collision term exhibits several important properties: (a) it includes a
nonlocal effect; (b) it conserves the mean field energy; (c) it satisfies the H
theorem; (d) its effect vanishes in each local equilibrium region with the same
temperature. When the system reaches a global equilibrium state, the collision
term completely converges to zero all over the system. | cond-mat_stat-mech |
Universality and criticality of a second-order granular
solid-liquid-like phase transition: We experimentally study the critical properties of the non-equilibrium
solid-liquid-like transition that takes place in vibrated granular matter. The
critical dynamics is characterized by the coupling of the density field with
the bond-orientational order parameter $Q_4$, which measures the degree of
local crystallization. Two setups are compared, which present the transition at
different critical accelerations as a a result of modifying the energy
dissipation parameters. In both setups five independent critical exponents are
measured, associated to different properties of $Q_4$: the correlation length,
relaxation time, vanishing wavenumber limit (static susceptibility), the
hydrodynamic regime of the pair correlation function, and the amplitude of the
order parameter. The respective critical exponents agree in both setups and are
given by $\nu_{\perp} = 1$, $\nu_{\parallel} = 2$, $\gamma = 1$, $\eta \approx
0.6 - 0.67$, and $\beta=1/2$, whereas the dynamical critical exponent is $z =
\nu_{\parallel}/\nu_{\perp} = 2$. The agreement on five exponents is an exigent
test for the universality of the transition. Thus, while dissipation is
strictly necessary to form the crystal, the path the system undergoes towards
the phase separation is part of a well defined universality class. In fact, the
local order shows critical properties while density does not. Being the later
conserved, the appropriate model that couples both is model C in the Hohenberg
and Halperin classification. The measured exponents are in accord with the
non-equilibrium extension to model C if we assume that $\alpha$, the exponent
associated in equilibrium to the specific heat divergence but with no
counterpart in this non-equilibrium experiment, vanishes. | cond-mat_stat-mech |
Equilibrium sampling of hard spheres up to the jamming density and
beyond: We implement and optimize a particle-swap Monte-Carlo algorithm that allows
us to thermalize a polydisperse system of hard spheres up to
unprecedentedly-large volume fractions, where \revise{previous} algorithms and
experiments fail to equilibrate. We show that no glass singularity intervenes
before the jamming density, which we independently determine through two
distinct non-equilibrium protocols. We demonstrate that equilibrium fluid and
non-equilibrium jammed states can have the same density, showing that the
jamming transition cannot be the end-point of the fluid branch. | cond-mat_stat-mech |
The Mixed Spin 3 - Spin 3/2 Ferrimagnetic Ising Model on Cellular
Automaton: The mixed spin 3- spin 3/2 Ising model has been simulated using cooling
algorithm on cellular automaton (CA). The simulations have been made in the
interval -6<=D<=6 for J=1 for the square lattices with periodic boundary
conditions. The ground state phase diagram of the model has different type
ferrimagnetic orderings. Through D/J=2 line, compensation points occurs at
kT/J=0. The values of the critical exponents ( {\nu}, {\alpha}, {\beta} and
{\gamma}) are estimated within the framework of the finite-size scaling theory
and power law relations for selected D/J values (-2, 0, 1, 2 and 4). The
estimated critical exponent values are in a good agreement with their universal
values of the two dimensional Ising model. | cond-mat_stat-mech |
Hamiltonian dynamics of the two-dimensional lattice phi^4 model: The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional
square lattice is investigated by means of numerical simulations. The
macroscopic observables are computed as time averages. The results clearly
reveal the presence of the continuous phase transition at a finite energy
density and are consistent both qualitatively and quantitatively with the
predictions of equilibrium statistical mechanics. The Hamiltonian microscopic
dynamics also exhibits critical slowing down close to the transition. Moreover,
the relationship between chaos and the phase transition is considered, and
interpreted in the light of a geometrization of dynamics. | cond-mat_stat-mech |
Magnitude-Dependent Omori Law: Empirical Study and Theory: We propose a new physically-based ``multifractal stress activation'' model of
earthquake interaction and triggering based on two simple ingredients: (i) a
seismic rupture results from activated processes giving an exponential
dependence on the local stress; (ii) the stress relaxation has a long memory.
The combination of these two effects predicts in a rather general way that
seismic decay rates after mainshocks follow the Omori law 1/t^p with exponents
p linearly increasing with the magnitude M of the mainshock and the inverse
temperature. We carefully test the prediction on the magnitude dependence of p
by a detailed analysis of earthquake sequences in the Southern California
Earthquake catalog. We find power law relaxations of seismic sequences
triggered by mainshocks with exponents p increasing with the mainshock
magnitude by approximately 0.1-0.15 for each magnitude unit increase, from
p(M=3) \approx 0.6 to p(M=7) \approx 1.1, in good agreement with the prediction
of the multifractal model. The results are robust with respect to different
time intervals, magnitude ranges and declustering methods. When applied to
synthetic catalogs generated by the ETAS (Epidemic-Type Aftershock Sequence)
model constituting a strong null hypothesis with built-in magnitude-independent
$p$-values, our procedure recovers the correct magnitude-independent p-values.
Our analysis thus suggests that a new important fact of seismicity has been
unearthed. We discuss alternative interpretations of the data and describe
other predictions of the model. | cond-mat_stat-mech |
Totally asymmetric limit for models of heat conduction: We consider one dimensional weakly asymmetric boundary driven models of heat
conduction. In the cases of a constant diffusion coefficient and of a quadratic
mobility we compute the quasi-potential that is a non local functional obtained
by the solution of a variational problem. This is done using the dynamic
variational approach of the macroscopic fluctuation theory \cite{MFT}. The case
of a concave mobility corresponds essentially to the exclusion model that has
been discussed in \cite{Lag,CPAM,BGLa,ED}. We consider here the convex case
that includes for example the Kipnis-Marchioro-Presutti (KMP) model and its
dual (KMPd) \cite{KMP}. This extends to the weakly asymmetric regime the
computations in \cite{BGL}. We consider then, both microscopically and
macroscopically, the limit of large external fields. Microscopically we discuss
some possible totally asymmetric limits of the KMP model. In one case the
totally asymmetric dynamics has a product invariant measure. Another possible
limit dynamics has instead a non trivial invariant measure for which we give a
duality representation. Macroscopically we show that the quasi-potentials of
KMP and KMPd, that for any fixed external field are non local, become local in
the limit. Moreover the dependence on one of the external reservoirs
disappears. For models having strictly positive quadratic mobilities we obtain
instead in the limit a non local functional having a structure similar to the
one of the boundary driven asymmetric exclusion process. | cond-mat_stat-mech |
Renormalized Multicanonical Sampling: For a homogeneous system divisible into identical, weakly interacting
subsystems, the muticanonical procedure can be accelerated if it is first
applied to determine of the density of states for a single subsystem. This
result is then employed to approximate the state density of a subsystem with
twice the size that forms the starting point of a new multicanonical iteration.
Since this compound subsystem interacts less on average with its environment,
iterating this sequence of steps rapidly generates the state density of the
full system. | cond-mat_stat-mech |
A weighted planar stochastic lattice with scale-free, small-world and
multifractal properties: We investigate a class of weighted planar stochastic lattice (WPSL1) created
by random sequential nucleation of seed from which a crack is grown parallel to
one of the sides of the chosen block and ceases to grow upon hitting another
crack. It results in the partitioning of the square into contiguous and
non-overlapping blocks. Interestingly, we find that the dynamics of WPSL1 is
governed by infinitely many conservation laws and each of the conserved
quantities, except the trivial conservation of total mass or area, is a
multifractal measure. On the other hand, the dual of the lattice is a
scale-free network as its degree distribution exhibits a power-law $P(k)\sim
k^{-\gamma}$ with $\gamma=4.13$. The network is also a small-world network as
we find that (i) the total clustering coefficient $C$ is high and independent
of the network size and (ii) the mean geodesic path length grows
logarithmically with $N$. Besides, the clustering coefficient $C_k$ of the
nodes which have degree $k$ decreases exactly as $2/(k-1)$ revealing that it is
also a nested hierarchical network. | cond-mat_stat-mech |
Transport Equations from Liouville Equations for Fractional Systems: We consider dynamical systems that are described by fractional power of
coordinates and momenta. The fractional powers can be considered as a
convenient way to describe systems in the fractional dimension space. For the
usual space the fractional systems are non-Hamiltonian. Generalized transport
equation is derived from Liouville and Bogoliubov equations for fractional
systems. Fractional generalization of average values and reduced distribution
functions are defined. Hydrodynamic equations for fractional systems are
derived from the generalized transport equation. | cond-mat_stat-mech |
Topological squashed entanglement: nonlocal order parameter for
one-dimensional topological superconductors: Identifying entanglement-based order parameters characterizing topological
systems, in particular topological superconductors and topological insulators,
has remained a major challenge for the physics of quantum matter in the last
two decades. Here we show that the end-to-end, long-distance, bipartite
squashed entanglement between the edges of a many-body system, defined in terms
of the edge-to-edge quantum conditional mutual information, is the natural
nonlocal order parameter for topological superconductors in one dimension as
well as in quasi one-dimensional geometries. For the Kitaev chain in the entire
topological phase, the edge squashed entanglement is quantized to log(2)/2,
half the maximal Bell-state entanglement, and vanishes in the trivial phase.
Such topological squashed entanglement exhibits the correct scaling at the
quantum phase transition, is stable in the presence of interactions, and is
robust against disorder and local perturbations. Edge quantum conditional
mutual information and edge squashed entanglement defined with respect to
different multipartitions discriminate topological superconductors from
symmetry breaking magnets, as shown by comparing the fermionic Kitaev chain and
the spin-1/2 Ising model in transverse field. For systems featuring multiple
topological phases with different numbers of edge modes, like the quasi 1D
Kitaev ladder, topological squashed entanglement counts the number of Majorana
excitations and distinguishes the different topological phases of the system.
In fact, we show that the edge quantum conditional mutual information and the
edge squashed entanglement remain valid detectors of topological
superconductivity even for systems, like the Kitaev tie with long-range
hopping, featuring geometrical frustration and a suppressed bulk-edge
correspondence. | cond-mat_stat-mech |
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