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A first--order irreversible thermodynamic approach to a simple energy
converter: Several authors have shown that dissipative thermal cycle models based on
Finite-Time Thermodynamics exhibit loop-shaped curves of power output versus
efficiency, such as it occurs with actual dissipative thermal engines. Within
the context of First-Order Irreversible Thermodynamics (FOIT), in this work we
show that for an energy converter consisting of two coupled fluxes it is also
possible to find loop-shaped curves of both power output and the so-called
ecological function against efficiency. In a previous work Stucki [J.W. Stucki,
Eur. J. Biochem. vol. 109, 269 (1980)] used a FOIT-approach to describe the
modes of thermodynamic performance of oxidative phosphorylation involved in
ATP-synthesis within mithochondrias. In that work the author did not use the
mentioned loop-shaped curves and he proposed that oxidative phosphorylation
operates in a steady state simultaneously at minimum entropy production and
maximum efficiency, by means of a conductance matching condition between
extreme states of zero and infinite conductances respectively. In the present
work we show that all Stucki's results about the oxidative phosphorylation
energetics can be obtained without the so-called conductance matching
condition. On the other hand, we also show that the minimum entropy production
state implies both null power output and efficiency and therefore this state is
not fulfilled by the oxidative phosphorylation performance. Our results suggest
that actual efficiency values of oxidative phosphorylation performance are
better described by a mode of operation consisting in the simultaneous
maximization of the so-called ecological function and the efficiency. | cond-mat_stat-mech |
The N-steps Invasion Percolation Model: A new kind of invasion percolation is introduced in order to take into
account the inertia of the invader fluid. The inertia strength is controlled by
the number N of pores (or steps) invaded after the perimeter rupture. The new
model belongs to a different class of universality with the fractal dimensions
of the percolating clusters depending on N. A blocking phenomenon takes place
in two dimensions. It imposes an upper bound value on N. For pore sizes larger
than the critical threshold, the acceptance profile exhibits a permanent tail. | cond-mat_stat-mech |
ac-driven Brownian motors: a Fokker-Planck treatment: We consider a primary model of ac-driven Brownian motors, i.e., a classical
particle placed in a spatial-time periodic potential and coupled to a heat
bath. The effects of fluctuations and dissipations are studied by a
time-dependent Fokker-Planck equation. The approach allows us to map the
original stochastic problem onto a system of ordinary linear algebraic
equations. The solution of the system provides complete information about
ratchet transport, avoiding such disadvantages of direct stochastic
calculations as long transients and large statistical fluctuations. The
Fokker-Planck approach to dynamical ratchets is instructive and opens the space
for further generalizations. | cond-mat_stat-mech |
A kinetic Ising model study of dynamical correlations in confined
fluids: Emergence of both fast and slow time scales: Experiments and computer simulation studies have revealed existence of rich
dynamics in the orientational relaxation of molecules in confined systems such
as water in reverse micelles, cyclodextrin cavities and nano-tubes. Here we
introduce a novel finite length one dimensional Ising model to investigate the
propagation and the annihilation of dynamical correlations in finite systems
and to understand the intriguing shortening of the orientational relaxation
time that has been reported for small sized reverse micelles. In our finite
sized model, the two spins at the two end cells are oriented in the opposite
directions, to mimic the effects of surface that in real system fixes water
orientation in the opposite directions. This produces opposite polarizations to
propagate inside from the surface and to produce bulk-like condition at the
centre. This model can be solved analytically for short chains. For long chains
we solve the model numerically with Glauber spin flip dynamics (and also with
Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely
reproduces many of the features observed in experiments. Due to the destructive
interference among correlations that propagate from the surface to the core,
one of the rotational relaxation time components decays faster than the bulk.
In general, the relaxation of spins is non-exponential due to the interplay
between various interactions. In the limit of strong coupling between the spins
or in the limit of low temperature, the nature of relaxation of the spins
undergoes a qualitative change with the emergence of a homogeneous dynamics
where decay is predominantly exponential, again in agreement with experiments. | cond-mat_stat-mech |
A Bottom-Up Model of Self-Organized Criticality on Networks: The Bak-Tang-Wiesenfeld (BTW) sandpile process is an archetypal, stylized
model of complex systems with a critical point as an attractor of their
dynamics. This phenomenon, called self-organized criticality (SOC), appears to
occur ubiquitously in both nature and technology. Initially introduced on the
2D lattice, the BTW process has been studied on network structures with great
analytical successes in the estimation of macroscopic quantities, such as the
exponents of asymptotically power-law distributions. In this article, we take a
microscopic perspective and study the inner workings of the process through
both numerical and rigorous analysis. Our simulations reveal fundamental flaws
in the assumptions of past phenomenological models, the same models that
allowed accurate macroscopic predictions; we mathematically justify why
universality may explain these past successes. Next, starting from scratch, we
obtain microscopic understanding that enables mechanistic models; such models
can, for example, distinguish a cascade's area from its size. In the special
case of a 3-regular network, we use self-consistency arguments to obtain a
zero-parameters, mechanistic (bottom-up) approximation that reproduces
nontrivial correlations observed in simulations and that allows the study of
the BTW process on networks in regimes otherwise prohibitively costly to
investigate. We then generalize some of these results to configuration model
networks and explain how one could continue the generalization. The numerous
tools and methods presented herein are known to enable studying the effects of
controlling the BTW process and other self-organizing systems. More broadly,
our use of multitype branching processes to capture information bouncing
back-and-forth in a network could inspire analogous models of systems in which
consequences spread in a bidirectional fashion. | cond-mat_stat-mech |
Specific heats of quantum double-well systems: Specific heats of quantum systems with symmetric and asymmetric double-well
potentials have been calculated. In numerical calculations of their specific
heats, we have adopted the combined method which takes into account not only
eigenvalues of $\epsilon_n$ for $0 \leq n \leq N_m$ obtained by the
energy-matrix diagonalization but also their extrapolated ones for $N_m+1 \leq
n < \infty$ ($N_m=20$ or 30). Calculated specific heats are shown to be rather
different from counterparts of a harmonic oscillator. In particular, specific
heats of symmetric double-well systems at very low temperatures have the
Schottky-type anomaly, which is rooted to a small energy gap in low-lying
two-level eigenstates induced by a tunneling through the potential barrier. The
Schottky-type anomaly is removed when an asymmetry is introduced into the
double-well potential. It has been pointed out that the specific-heat
calculation of a double-well system reported by Feranchuk, Ulyanenkov and
Kuz'min [Chem. Phys. 157, 61 (1991)] is misleading because the zeroth-order
operator method they adopted neglects crucially important off-diagonal
contributions. | cond-mat_stat-mech |
Roughening Transition of Interfaces in Disordered Systems: The behavior of interfaces in the presence of both lattice pinning and random
field (RF) or random bond (RB) disorder is studied using scaling arguments and
functional renormalization techniques. For the first time we show that there is
a continuous disorder driven roughening transition from a flat to a rough state
for internal interface dimensions 2<D<4. The critical exponents are calculated
in an \epsilon-expansion. At the transition the interface shows a
superuniversal logarithmic roughness for both RF and RB systems. A transition
does not exist at the upper critical dimension D_c=4. The transition is
expected to be observable in systems with dipolar interactions by tuning the
temperature. | cond-mat_stat-mech |
Landau thermodynamic potential for BaTiO_3: In the paper, the description of the dielectric and ferroelectric properties
of BaTiO_3 single crystals using Landau thermodynamic potential is addressed.
Our results suggest that when using the sixth-power free energy expansion of
the thermodynamic potential, remarkably different values of the fourth-power
coefficient, \beta (the coefficient of P^4_i terms), are required to adequately
reproduce the nonlinear dielectric behavior of the paraelectric phase and the
electric field induced ferroelectric phase, respectively. In contrast, the
eighth-power expansion with a common set of coefficients enables a good
description for both phases at the same time. These features, together with the
data available in literature, strongly attest to the necessity of the
eighth-power terms in Landau thermodynamic potential of BaTiO_3. In addition,
the fourth-power coefficients, \beta and \xi (the coefficient of P^2_i P^2_j
terms), were evaluated from the nonlinear dielectric responses along [001],
[011], and [111] orientations in the paraelectric phase. Appreciable
temperature dependence was evidenced for both coefficients above T_C. Further
analysis on the linear dielectric response of the single domain crystal in the
tetragonal phase demonstrated that temperature dependent anharmonic
coefficients are also necessary for an adequate description of the dielectric
behavior in the ferroelectric phase. As a consequence, an eighth-power
thermodynamic potential, with some of the anharmonic coefficients being
temperature dependent, was proposed and compared with the existing potentials.
In general, the potential proposed in this work exhibits a higher quality in
reproducing the dielectric and ferroelectric properties of this prototypic
ferroelectric substance. | cond-mat_stat-mech |
Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg
model on the triangulated Kagome (triangles-in-triangles) lattice: The geometric frustration of the spin-1/2 Ising-Heisenberg model on the
triangulated Kagome (triangles-in-triangles) lattice is investigated within the
framework of an exact analytical method based on the generalized star-triangle
mapping transformation. Ground-state and finite-temperature phase diagrams are
obtained along with other exact results for the partition function, Helmholtz
free energy, internal energy, entropy, and specific heat, by establishing a
precise mapping relationship to the corresponding spin-1/2 Ising model on the
Kagome lattice. It is shown that the residual entropy of the disordered spin
liquid phase is for the quantum Ising-Heisenberg model significantly lower than
for its semi-classical Ising limit (S_0/N_T k_B = 0.2806 and 0.4752,
respectively), which implies that quantum fluctuations partially lift a
macroscopic degeneracy of the ground-state manifold in the frustrated regime.
The investigated model system has an obvious relevance to a series of polymeric
coordination compounds Cu_9X_2(cpa)_6 (X=F, Cl, Br and cpa=carboxypentonic
acid) for which we made a theoretical prediction about the temperature
dependence of zero-field specific heat. | cond-mat_stat-mech |
Building Entanglement Entropy out of Correlation Functions for
Interacting Fermions: We provide a prescription to construct R\'{e}nyi and von Neumann entropy of a
system of interacting fermions from a knowledge of its correlation functions.
We show that R\'{e}nyi entanglement entropy of interacting fermions in
arbitrary dimensions can be represented by a Schwinger Keldysh free energy on
replicated manifolds with a current between the replicas. The current is local
in real space and is present only in the subsystem which is not integrated out.
This allows us to construct a diagrammatic representation of entanglement
entropy in terms of connected correlators in the standard field theory with no
replicas. This construction is agnostic to how the correlators are calculated,
and one can use calculated, simulated or measured values of the correlators in
this formula. Using this diagrammatic representation, one can decompose
entanglement into contributions which depend on the one-particle correlator,
two particle correlator and so on. We provide analytic formula for the
one-particle contribution and a diagrammatic construction for higher order
contributions. We show how this construction can be extended for von-Neumann
entropy through analytic continuation. For a practical implementation of a
quantum state, where one usually has information only about few-particle
correlators, this provides an approximate way of calculating entanglement
commensurate with the limited knowledge about the underlying quantum state. | cond-mat_stat-mech |
Physical swap dynamics, shortcuts to relaxation and entropy production
in dissipative Rydberg gases: Dense Rydberg gases are out-of-equilibrium systems where strong
density-density interactions give rise to effective kinetic constraints. They
cause dynamic arrest associated with highly-constrained many-body
configurations, leading to slow relaxation and glassy behavior. Multi-component
Rydberg gases feature additional long-range interactions such as
excitation-exchange. These are analogous to particle swaps used to artificially
accelerate relaxation in simulations of atomistic models of classical glass
formers. In Rydberg gases, however, swaps are real physical processes, which
provide dynamical shortcuts to relaxation. They permit the accelerated approach
to stationarity in experiment and at the same time have an impact on the
non-equilibrium stationary state. In particular their interplay with radiative
decay processes amplifies irreversibility of the dynamics, an effect which we
quantify via the entropy production at stationarity. Our work highlights an
intriguing analogy between real dynamical processes in Rydberg gases and
artificial dynamics underlying advanced Monte Carlo methods. Moreover, it
delivers a quantitative characterization of the dramatic effect swaps have on
the structure and dynamics of their stationary state. | cond-mat_stat-mech |
Continuity Conditions for the Radial Distribution Function of
Square-Well Fluids: The continuity conditions of the radial distribution function g(r) and its
close relative the cavity function y(r) are studied in the context of the
Percus-Yevick (PY) integral equation for 3D square-well fluids. The cases
corresponding to a well width, (w-1)*d, equal to a fraction of the diameter of
the hard core, d/m, with m=1,2,3 have been considered. In these cases, it is
proved that the function y(r) and its first derivative are everywhere
continuous but eventually the derivative of some order becomes discontinuous at
the points (n+1)d/m, n=0,1,... . The order of continuity (the highest order
derivative of y(r) being continuous at a given point) is found to be
proportional to n in the first case (m=1) and to 2*n in the other two cases
(m=2,3), for large values of n. Moreover, derivatives of y(r) up to third order
are continuous at r=d and r=w*d for w=3/2 and w=4/3 but only the first
derivative is continuous for w=2. This can be understood as a non-linear
resonance effect. | cond-mat_stat-mech |
Route from discreteness to the continuum for the non-logarithmic
$q$-entropy: The existence and exact form of the continuum expression of the discrete
nonlogarithmic $q$-entropy is an important open problem in generalized
thermostatistics, since its possible lack implies that nonlogarithmic
$q$-entropy is irrelevant for the continuous classical systems. In this work,
we show how the discrete nonlogarithmic $q$-entropy in fact converges in the
continuous limit and the negative of the $q$-entropy with continuous variables
is demonstrated to lead to the (Csisz{\'a}r type) $q$-relative entropy just as
the relation between the continuous Boltzmann-Gibbs expression and the
Kullback-Leibler relative entropy. As a result, we conclude that there is no
obstacle for the applicability of the $q$-entropy to the continuous classical
physical systems. | cond-mat_stat-mech |
Extinction rates of established spatial populations: This paper deals with extinction of an isolated population caused by
intrinsic noise. We model the population dynamics in a "refuge" as a Markov
process which involves births and deaths on discrete lattice sites and random
migrations between neighboring sites. In extinction scenario I the zero
population size is a repelling fixed point of the on-site deterministic
dynamics. In extinction scenario II the zero population size is an attracting
fixed point, corresponding to what is known in ecology as Allee effect.
Assuming a large population size, we develop WKB (Wentzel-Kramers-Brillouin)
approximation to the master equation. The resulting Hamilton's equations encode
the most probable path of the population toward extinction and the mean time to
extinction. In the fast-migration limit these equations coincide, up to a
canonical transformation, with those obtained, in a different way, by Elgart
and Kamenev (2004). We classify possible regimes of population extinction with
and without an Allee effect and for different types of refuge and solve several
examples analytically and numerically. For a very strong Allee effect the
extinction problem can be mapped into the over-damped limit of theory of
homogeneous nucleation due to Langer (1969). In this regime, and for very long
systems, we predict an optimal refuge size that maximizes the mean time to
extinction. | cond-mat_stat-mech |
Entropy and forecasting complexity of hidden Markov models, matrix
product states, and observable operator models: In a series of three papers, Jurgens and Crutchfield recently proposed a
supposedly novel method to compute entropies of hidden Markov models (HMMs),
discussed in detail its relationship to iterated function systems, and applied
it to compute their ``ambiguity rates", a concept supposedly introduced by
Claude Shannon. We point out that the basic formalism is not new (it is the
well known ``forward algorithm" for HMMs), and that all three papers have also
serious other faults. | cond-mat_stat-mech |
Superoperator coupled cluster method for nonequilibrium density matrix: We develop a superoperator coupled cluster method for nonequilibrium open
many-body quantum systems described by the Lindblad master equation. The method
is universal and applicable to systems of interacting fermions, bosons or their
mixtures. We present a general theory and consider its application to the
problem of quantum transport through the system with electron-phonon
correlations. The results are assessed against the perturbation theory and
nonequilibrium configuration interaction theory calculations. | cond-mat_stat-mech |
Analysis of a generalised Boltzmann equation for anomalous diffusion
under time-dependent fields: The generalised Boltzmann equation which treats the combined localised and
delocalised nature of transport present in certain materials is extended to
accommodate time-dependent fields. In particular, AC fields are shown to be a
means to probe the trapping and detrapping rates of materials under certain
conditions. Conditions leading to dispersive transport are considered, and the
signature of fractional/anomalous diffusion under AC electric fields is
presented. | cond-mat_stat-mech |
Slow Kinetics of Brownian Maxima: We study extreme-value statistics of Brownian trajectories in one dimension.
We define the maximum as the largest position to date and compare maxima of two
particles undergoing independent Brownian motion. We focus on the probability
P(t) that the two maxima remain ordered up to time t, and find the algebraic
decay P ~ t^(-beta) with exponent beta=1/4. When the two particles have
diffusion constants D1 and D2, the exponent depends on the mobilities,
beta=(1/pi)arctan[sqrt(D2/D1)]. We also use numerical simulations to
investigate maxima of multiple particles in one dimension and the largest
extension of particles in higher dimensions. | cond-mat_stat-mech |
Low self-affine exponents of fracture surfaces of glass ceramics: The geometry of post mortem rough fracture surfaces of porous glass ceramics
made of sintered glass beads is shown experimentally to be self-affine with an
exponent zeta=0.40 (0.04) remarkably lower than the 'universal' value zeta=0.8
frequently measured for many materials. This low value of zeta is similar to
that found for sandstone samples of similar micro structure and is also
practically independent on the porosity phi in the range investigated (3% < phi
< 26%) as well as on the bead diameter d and of the crack growth velocity. In
contrast, the roughness amplitude normalized by d increases linearly with phi
while it is still independent, within experimental error, of d and of the crack
propagation velocity. An interpretation of this variation is suggested in terms
of a transition from transgranular to intergranular fracture propagation with
no influence, however, on the exponent zeta. | cond-mat_stat-mech |
Non-equilibrium dynamics in the quantum Brownian oscillator and the
second law of thermodynamics: We initially prepare a quantum linear oscillator weakly coupled to a bath in
equilibrium at an arbitrary temperature. We disturb this system by varying a
Hamiltonian parameter of the coupled oscillator, namely, either its spring
constant or mass according to an arbitrary but pre-determined protocol in order
to perform external work on it. We then derive a closed expression for the
reduced density operator of the coupled oscillator along this non-equilibrium
process as well as the exact expression pertaining to the corresponding
quasi-static process. This immediately allows us to analytically discuss the
second law of thermodynamics for non-equilibrium processes. Then we derive a
Clausius inequality and obtain its validity supporting the second law, as a
consistent generalization of the Clausius equality valid for the quasi-static
counterpart, introduced in [1]. | cond-mat_stat-mech |
Phase transitions in Ising models on directed networks: We examine Ising models with heat-bath dynamics on directed networks. Our
simulations show that Ising models on directed triangular and simple cubic
lattices undergo a phase transition that most likely belongs to the Ising
universality class. On the directed square lattice the model remains
paramagnetic at any positive temperature as already reported in some previous
studies. We also examine random directed graphs and show that contrary to
undirected ones, percolation of directed bonds does not guarantee ferromagnetic
ordering. Only above a certain threshold a random directed graph can support
finite-temperature ferromagnetic ordering. Such behaviour is found also for
out-homogeneous random graphs, but in this case the analysis of magnetic and
percolative properties can be done exactly. Directed random graphs also differ
from undirected ones with respect to zero-temperature freezing. Only at low
connectivity they remain trapped in a disordered configuration. Above a certain
threshold, however, the zero-temperature dynamics quickly drives the model
toward a broken symmetry (magnetized) state. Only above this threshold, which
is almost twice as large as the percolation threshold, we expect the Ising
model to have a positive critical temperature. With a very good accuracy, the
behaviour on directed random graphs is reproduced within a certain approximate
scheme. | cond-mat_stat-mech |
Classical stochastic approach to quantum mechanics and quantum
thermodynamics: We derive the equations of quantum mechanics and quantum thermodynamics from
the assumption that a quantum system can be described by an underlying
classical system of particles. Each component $\phi_j$ of the wave vector is
understood as a stochastic complex variable whose real and imaginary parts are
proportional to the coordinate and momentum associated to a degree of freedom
of the underlying classical system. From the classical stochastic equations of
motion, we derive a general equation for the covariance matrix of the wave
vector which turns out to be of the Lindblad type. When the noise changes only
the phase of $\phi_j$, the Schr\"odinger and the quantum Liouville equation are
obtained. The component $\psi_j$ of the wave vector obeying the Schr\"odinger
equation is related to stochastic wave vector by
$|\psi_j|^2=\langle|\phi_j|^2\rangle$. | cond-mat_stat-mech |
Pseudo-$ε$ Expansion and Renormalized Coupling Constants at
Criticality: Universal values of dimensional effective coupling constants $g_{2k}$ that
determine nonlinear susceptibilities $\chi_{2k}$ and enter the scaling equation
of state are calculated for $n$-vector field theory within the
pseudo-$\epsilon$ expansion approach. Pseudo-$\epsilon$ expansions for $g_6$
and $g_8$ at criticality are derived for arbitrary $n$. Analogous series for
ratios $R_6 = g_6/g_4^2$ and $R_8 = g_8/g_4^3$ figuring in the equation of
state are also found and the pseudo-$\epsilon$ expansion for Wilson fixed point
location $g_{4}^*$ descending from the six-loop RG expansion for
$\beta$-function is reported. Numerical results are presented for $0 \le n \le
64$ with main attention paid to physically important cases $n = 0, 1, 2, 3$.
Pseudo-$\epsilon$ expansions for quartic and sextic couplings have rapidly
diminishing coefficients, so Pad\'e resummation turns out to be sufficient to
yield high-precision numerical estimates. Moreover, direct summation of these
series with optimal truncation gives the values of $g_4^*$ and $R_6^*$ almost
as accurate as those provided by Pad\'e technique. Pseudo-$\epsilon$ expansion
estimates for $g_8^*$ and $R_8^*$ are found to be much worse than that for the
lower-order couplings independently on the resummation method employed.
Numerical effectiveness of the pseudo-$\epsilon$ expansion approach in two
dimensions is also studied. Pseudo-$\epsilon$ expansion for $g_4^*$ originating
from the five-loop RG series for $\beta$-function of 2D $\lambda\phi^4$ field
theory is used to get numerical estimates for $n$ ranging from 0 to 64. The
approach discussed gives accurate enough values of $g_{4}^*$ down to $n = 2$
and leads to fair estimates for Ising and polymer ($n = 0$) models. | cond-mat_stat-mech |
Cluster formation and anomalous fundamental diagram in an ant trail
model: A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35,
L573 (2002)}), motivated by the motions of ants in a trail, is investigated in
detail in this paper. The flux of ants in this model is sensitive to the
probability of evaporation of pheromone, and the average speed of the ants
varies non-monotonically with their density. This remarkable property is
analyzed here using phenomenological and microscopic approximations thereby
elucidating the nature of the spatio-temporal organization of the ants. We find
that the observations can be understood by the formation of loose clusters,
i.e. space regions of enhanced, but not maximal, density. | cond-mat_stat-mech |
Circuits in random graphs: from local trees to global loops: We compute the number of circuits and of loops with multiple crossings in
random regular graphs. We discuss the importance of this issue for the validity
of the cavity approach. On the one side we obtain analytic results for the
infinite volume limit in agreement with existing exact results. On the other
side we implement a counting algorithm, enumerate circuits at finite N and draw
some general conclusions about the finite N behavior of the circuits. | cond-mat_stat-mech |
First quantum corrections for a hydrodynamics of a nonideal Bose gas: In the paper we consider a hydrodynamical description of a nonideal Bose gas
in one-loop approximation. We calculate an effective action which consists of
mean field contributions and first quantum correction. This provides the
equations of motion for the density and velocity of the gas where both mean
field contributions and fluctuations are presented. To fulfill the calculation
we make use of the formalism of functional integrals to map the problem to a
problem of quantum gravity to benefit from a well-developed technique in this
field. This effective action provides all correlation functions for the system
and is a basis for a consideration of dynamics of the gas. Response functions
are briefly discussed. Applications to the trapped bosons are reviewed.
Together with Ref.\cite{IS} the paper provide complete description of the
condensate fraction and the deplition in the case of Bose condensed gases. | cond-mat_stat-mech |
An appetizer to modern developments on the Kardar-Parisi-Zhang
universality class: The Kardar-Parisi-Zhang (KPZ) universality class describes a broad range of
non-equilibrium fluctuations, including those of growing interfaces, directed
polymers and particle transport, to name but a few. Since the year 2000, our
understanding of the one-dimensional KPZ class has been completely renewed by
mathematical physics approaches based on exact solutions. Mathematical physics
has played a central role since then, leading to a myriad of new developments,
but their implications are clearly not limited to mathematics -- as a matter of
fact, it can also be studied experimentally. The aim of these lecture notes is
to provide an introduction to the field that is accessible to non-specialists,
reviewing basic properties of the KPZ class and highlighting main physical
outcomes of mathematical developments since the year 2000. It is written in a
brief and self-contained manner, with emphasis put on physical intuitions and
implications, while only a small (and mostly not the latest) fraction of
mathematical developments could be covered. Liquid-crystal experiments by the
author and coworkers are also reviewed. | cond-mat_stat-mech |
Landau Theory for the Mpemba Effect Through Phase Transitions: The Mpemba effect describes the situation in which a hot system cools faster
than an identical copy that is initiated at a colder temperature. In many of
the experimental observations of the effect, e.g. in water and clathrate
hydrates, it is defined by the phase transition timing. However, none of the
theoretical investigations so far considered the timing of the phase
transition, and most of the abstract models used to explore the Mpemba effect
do not have a phase transition. We use the phenomenological Landau theory for
phase transitions to identify the second order phase transition time, and
demonstrate with a concrete example that a Mpemba effect can exist in such
models. | cond-mat_stat-mech |
Isomorphic classical molecular dynamics model for an excess electron in
a supercritical fluid: Ring polymer molecular dynamics (RPMD) is used to directly simulate the
dynamics of an excess electron in a supercritical fluid over a broad range of
densities. The accuracy of the RPMD model is tested against numerically exact
path integral statistics through the use of analytical continuation techniques.
At low fluid densities, the RPMD model substantially underestimates the
contribution of delocalized states to the dynamics of the excess electron.
However, with increasing solvent density, the RPMD model improves, nearly
satisfying analytical continuation constraints at densities approaching those
of typical liquids. In the high density regime, quantum dispersion
substantially decreases the self-diffusion of the solvated electron.
In this regime where the dynamics of the electron is strongly coupled to the
dynamics of the atoms in the fluid, trajectories that can reveal diffusive
motion of the electron are long in comparison to $\beta\hbar$. | cond-mat_stat-mech |
Arrested States formed on Quenching Spin Chains with Competing
Interactions and Conserved Dynamics: We study the effects of rapidly cooling to T = 0 a spin chain with conserved
dynamics and competing interactions. Depending on the degree of competition,
the system is found to get arrested in different kinds of metastable states.
The most interesting of these has an inhomogeneous mixture of interspersed
active and quiescent regions. In this state, the steady-state autocorrelation
function decays as a stretched exponential $\sim
\exp(-{(t/\tau_{o})}^{{1}\over{3}})$, and there is a two-step relaxation to
equilibrium when the temperature is raised slightly. | cond-mat_stat-mech |
Reply to the comment on: "Thermostatistics of Overdamped Motion of
Interacting Particles" [arXiv:1104.0697] by Y. Levin and R. Pakter: We show that the comment [arXiv:1104.0697] by Levin and Pakter on our work
[arXiv:1008.1421] is conceptually unfounded, contains misleading
interpretations, and is based on results of questionable applicability. We
initially provide arguments to evince that, inexplicably, these authors simply
choose to categorically dismiss our elaborated and solid conceptual approach,
results and analysis, without employing any fundamental concepts or tools from
Statistical Physics. We then demonstrate that the results of Levin and Pakter
do not present any evidence against, but rather corroborates, our conclusions.
In fact, the results shown in their comment correspond to a confining potential
that is 1000 times stronger than the typical valued utilized in our study,
therefore explaining the discrepancy between their results and ours.
Furthermore, in this regime where higher vortex densities are involved, vortex
cores might get so close to each other that can no longer be treated as
point-like defects. As a consequence, Ginzburg-Landau equations should be
employed instead, meaning that the physical conditions implied by the results
of Levin and Pakter should be considered with caution in the context of the
Physics of interacting superconducting vortexes. | cond-mat_stat-mech |
Determination of Nonequilibrium Temperature and Pressure using Clausius
Equality in a State with Memory: A Simple Model Calculation: Use of the extended definition of heat dQ=deQ+diQ converts the Clausius
inequality dS greater than or equal to deQ/T0 into an equality dS=dQ/T
involving the nonequilibrium temperature T of the system having the
conventional interpretation that heat flows from hot to cold. The equality is
applied to the exact quantum evolution of a 1-dimensional ideal gas free
expansion. In a first ever calculation of its kind in an expansion which
retains the memory of initial state, we determine the nonequilibrium
temperature T and pressure P, which are then compared with the ratio P/T
obtained by an independent method to show the consistency of the nonequilibrium
formulation. We find that the quantum evolution by itself cannot eliminate the
memory effect.cannot eliminate the memory effect; hence, it cannot thermalize
the system. | cond-mat_stat-mech |
Some measure theory on stacks of graphs: We apply a theorem of Wick to rewrite certain classes of exponential measures
on random graphs as integrals of Feynman-Gibbs type, on the real line. The
analytic properties of these measures can then be studied in terms of phase
transitions; spaces of scale-free trees are a particularly interesting example. | cond-mat_stat-mech |
Entanglement dynamics in critical random quantum Ising chain with
perturbations: We simulate the entanglement dynamics in a critical random quantum Ising
chain with generic perturbations using the time-evolving block decimation
algorithm. Starting from a product state, we observe super-logarithmic growth
of entanglement entropy with time. The numerical result is consistent with the
analytical prediction of Vosk and Altman using a real-space renormalization
group technique. | cond-mat_stat-mech |
Physical insights from imaginary-time density--density correlation
functions: The accurate theoretical description of the dynamic properties of correlated
quantum many-body systems such as the dynamic structure factor
$S(\mathbf{q},\omega)$ constitutes an important task in many fields.
Unfortunately, highly accurate quantum Monte Carlo methods are usually
restricted to the imaginary time domain, and the analytic continuation of the
imaginary time density--density correlation function $F(\mathbf{q},\tau)$ to
real frequencies is a notoriously hard problem. In this work, we argue that no
such analytic continuation is required as $F(\mathbf{q},\tau)$ contains, by
definition, the same physical information as $S(\mathbf{q},\omega)$, only in an
unfamiliar representation. Specifically, we show how we can directly extract
key information such as the temperature or quasi-particle excitation energies
from the $\tau$-domain, which is highly relevant for equation-of-state
measurements of matter under extreme conditions. As a practical example, we
consider \emph{ab initio} path integral Monte Carlo results for the uniform
electron gas (UEG), and demonstrate that even nontrivial processes such as the
\emph{roton feature} of the UEG at low density straightforwardly manifest in
$F(\mathbf{q},\tau)$. In fact, directly working in the $\tau$-domain is
advantageous for many reasons and holds the enticing promise for unprecedented
agreement between theory and experiment. | cond-mat_stat-mech |
Statistical Mechanics of Double sinh-Gordon Kinks: We study the classical thermodynamics of the double sinh-Gordon (DSHG) theory
in 1+1 dimensions. This model theory has a double well potential, thus allowing
for the existence of kinks and antikinks. Though it is nonintegrable, the DSHG
model is remarkably amenable to analysis. Below we obtain exact single kink and
kink lattice solutions as well as the asymptotic kink-antikink interaction. In
the continuum limit, finding the classical partition function is equivalent to
solving for the ground state of a Schrodinger-like equation obtained via the
transfer integral method. For the DSHG model, this equation turns out to be
quasi-exactly solvable. We exploit this property to obtain exact energy
eigenvalues and wavefunctions for several temperatures both above and below the
symmetry breaking transition temperature. The availability of exact results
provides an excellent testing ground for large scale Langevin simulations. The
probability distribution function (PDF) calculated from Langevin dynamics is
found to be in striking agreement with the exact PDF obtained from the ground
state wavefunction. This validation points to the utility of a PDF-based
computation of thermodynamics utilizing Langevin methods. In addition to the
PDF, field-field and field fluctuation correlation functions were computed and
also found to be in excellent agreement with the exact results. | cond-mat_stat-mech |
Friction effects and clogging in a cellular automaton model for
pedestrian dynamics: We investigate the role of conflicts in pedestrian traffic, i.e. situations
where two or more people try to enter the same space. Therefore a recently
introduced cellular automaton model for pedestrian dynamics is extended by a
friction parameter $\mu$. This parameter controls the probability that the
movement of all particles involved in a conflict is denied at one time step. It
is shown that these conflicts are not an undesirable artefact of the parallel
update scheme, but are important for a correct description of the dynamics. The
friction parameter $\mu$ can be interpreted as a kind of internal local
pressure between the pedestrians which becomes important in regions of high
density, ocurring e.g. in panic situations. We present simulations of the
evacuation of a large room with one door. It is found that friction has not
only quantitative effects, but can also lead to qualitative changes, e.g. of
the dependence of the evacuation time on the system parameters. We also observe
similarities to the flow of granular materials, e.g. arching effects. | cond-mat_stat-mech |
The Dilemma of Bose Solids: is He Supersolid?: Nearly a decade ago the old controversy about possible superfluid flow in the
ground state of solid He4 was revived by the apparent experimental observation
of such superflow. Although the experimentalists have recently retracted, very
publicly, some of the observations on which such a claim was based, other
confirming observations of which there is no reason for doubt remain on the
record. Meanwhile theoretical arguments bolstered by some experimental evidence
strongly favor the existence of supersolidity in the Bose-Hubbard model, and
these arguments would seem to extend to solid He. The true situation thus is
apparently extraordinarily opaque. The situation is complicated by the fact
that all accurate simulation studies on Heuse the uniform sign hypothesis which
confines them to the phase-coherent state, which is, in principle, supersolid,
so that no accurate simulations of the true, classical solid exist. There is
great confusion as to the nature of the ground state wave-function for a bose
quantum solid, and we suggest that until that question is cleared up none of
these dilemmas will be resolved. | cond-mat_stat-mech |
Collective dynamics in systems of active Brownian particles with
dissipative interactions: We use computer simulations to study the onset of collective motion in
systems of interacting active particles. Our model is a swarm of active
Brownian particles with internal energy depot and interactions inspired by the
dissipative particle dynamics method, imposing pairwise friction force on the
nearest neighbours. We study orientational ordering in a 2D system as a
function of energy influx rate and particle density. The model demonstrates a
transition into the ordered state on increasing the particle density and
increasing the input power. Although both the alignment mechanism and the
character of individual motion in our model differ from those in the
well-studied Vicsek model, it demonstrates identical statistical properties and
phase behaviour. | cond-mat_stat-mech |
Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids: A novel stochastic fluid model is proposed with non-ideal structure factor
consistent with compressibility, and adjustable transport coefficients. This
Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the
Direct Simulation Monte Carlo (DSMC) algorithm and has several computational
advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD
results in an equation of state and pair correlation function identical to that
of a deterministic Hamiltonian system of penetrable spheres interacting with
linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD
fluid is verified for the Brownian motion of a nano-particle suspended in a
compressible solvent. | cond-mat_stat-mech |
Evolution of the System with Singular Multiplicative Noise: The governed equations for the order parameter, one-time and two-time
correlators are obtained on the basis of the Langevin equation with the white
multiplicative noise which amplitude $x^{a}$ is determined by an exponent
$0<a<1$ ($x$ being a stochastic variable). It turns out that equation for
autocorrelator includes an anomalous average of the power-law function with the
fractional exponent $2a$. Determination of this average for the stochastic
system with a self-similar phase space is performed. It is shown that at
$a>1/2$, when the system is disordered, the correlator behaves
non-monotonically in the course of time, whereas the autocorrelator is
increased monotonically. At $a<1/2$ the phase portrait of the system evolution
divides into two domains: at small initial values of the order parameter, the
system evolves to a disordered state, as above; within the ordered domain it is
attracted to the point having the finite values of the autocorrelator and order
parameter. The long-time asymptotes are defined to show that, within the
disordered domain, the autocorrelator decays hyperbolically and the order
parameter behaves as the power-law function with fractional exponent $-2(1-a)$.
Correspondingly, within the ordered domain, the behavior of both dependencies
is exponential with an index proportional to $-t\ln t$. | cond-mat_stat-mech |
Density-feedback control in traffic and transport far from equilibrium: A bottleneck situation in one-lane traffic-flow is typically modelled with a
constant demand of entering cars. However, in practice this demand may depend
on the density of cars in the bottleneck. The present paper studies a simple
bimodal realization of this mechanism to which we refer to as density-feedback
control (DFC): If the actual density in the bottleneck is above a certain
threshold, the reservoir density of possibly entering cars is reduced to a
different constant value. By numerical solution of the discretized viscid
Burgers equation a rich stationary phase diagram is found. In order to maximize
the flow, which is the goal of typical traffic-management strategies, we find
the optimal choice of the threshold. Analytical results are verified by
computer simulations of the microscopic TASEP with DFC. | cond-mat_stat-mech |
A Langevin canonical approach to the dynamics of chiral two level
systems. Thermal averages and heat capacity: A Langevin canonical framework for a chiral two--level system coupled to a
bath of harmonic oscillators is developed within a coupling scheme different to
the well known spin-boson model. Thermal equilibrium values are reached at
asymptotic times by solving the corresponding set of non--linear coupled
equations in a Markovian regime. In particular, phase difference thermal values
(or, equivalently, the so--called coherence factor) and heat capacity through
energy fluctuations are obtained and discussed in terms of tunneling rates and
asymmetries. | cond-mat_stat-mech |
Generalized Tsallis Thermostatistics of Magnetic Systems: In this study, our effort is to introduce Tsallis thermostatistics in some
details and to give a brief review of the magnetic systems which have been
studied in the frame of this formalism. | cond-mat_stat-mech |
The ground state energy of the Edwards-Anderson spin glass model with a
parallel tempering Monte Carlo algorithm: We study the efficiency of parallel tempering Monte Carlo technique for
calculating true ground states of the Edwards-Anderson spin glass model.
Bimodal and Gaussian bond distributions were considered in two and
three-dimensional lattices. By a systematic analysis we find a simple formula
to estimate the values of the parameters needed in the algorithm to find the GS
with a fixed average probability. We also study the performance of the
algorithm for single samples, quantifying the difference between samples where
the GS is hard, or easy, to find. The GS energies we obtain are in good
agreement with the values found in the literature. Our results show that the
performance of the parallel tempering technique is comparable to more powerful
heuristics developed to find the ground state of Ising spin glass systems. | cond-mat_stat-mech |
Random walks on uniform and non-uniform combs and brushes: We consider random walks on comb- and brush-like graphs consisting of a base
(of fractal dimension $D$) decorated with attached side-groups. The graphs are
also characterized by the fractal dimension $D_a$ of a set of anchor points
where side-groups are attached to the base. Two types of graphs are considered.
Graphs of the first type are uniform in the sense that anchor points are
distributed periodically over the base, and thus form a subset of the base with
dimension $D_a=D$. Graphs of the second type are decorated with side-groups in
a regular yet non-uniform way: the set of anchor points has fractal dimension
smaller than that of the base, $D_a<D$. For uniform graphs, a qualitative
method for evaluating the sub-diffusion exponent suggested by Forte et al. for
combs ($D=1$) is extended for brushes ($D>1$) and numerically tested for the
Sierpinski brush (with the base and anchor set built on the same Sierpinski
gasket). As an example of nonuniform graphs we consider the Cantor comb
composed of a one-dimensional base and side-groups, the latter attached to the
former at anchor points forming the Cantor set. A peculiar feature of this and
other nonuniform systems is a long-lived regime of super-diffusive transport
when side-groups are of a finite size. | cond-mat_stat-mech |
Decay of Metastable States: Sharp Transition from Quantum to Classical
Behavior: The decay rate of metastable states is determined at high temperatures by
thermal activation, whereas at temperatures close to zero quantum tunneling is
relevant. At some temperature $T_{c}$ the transition from classical to
quantum-dominated decay occurs. The transition can be first-order like, with a
discontinuous first derivative of the Euclidean action, or smooth with only a
second derivative developing a jump. In the former case the crossover
temperature $T_{c}$ cannot be calculated perturbatively and must be found as
the intersection point of the Euclidean actions calculated at low and high
temperatures. In this paper we present a sufficient criterion for a first-order
transition in tunneling problems and apply it to the problem of the tunneling
of strings. It is shown that the problem of the depinning of a massive string
from a linear defect in the presence of an arbitrarily strong dissipation
exhibits a first-order transition. | cond-mat_stat-mech |
Nonlinear response and emerging nonequilibrium micro-structures for
biased diffusion in confined crowding environments: We study analytically the dynamics and the micro-structural changes of a host
medium caused by a driven tracer particle moving in a confined, quiescent
molecular crowding environment. Imitating typical settings of active
micro-rheology experiments, we consider here a minimal model comprising a
geometrically confined lattice system -- a two-dimensional strip-like or a
three-dimensional capillary-like -- populated by two types of hard-core
particles with stochastic dynamics -- a tracer particle driven by a constant
external force and bath particles moving completely at random. Resorting to a
decoupling scheme, which permits us to go beyond the linear-response
approximation (Stokes regime) for arbitrary densities of the lattice gas
particles, we determine the force-velocity relation for the tracer particle and
the stationary density profiles of the host medium particles around it. These
results are validated a posteriori by extensive numerical simulations for a
wide range of parameters. Our theoretical analysis reveals two striking
features: a) We show that, under certain conditions, the terminal velocity of
the driven tracer particle is a nonmonotonic function of the force, so that in
some parameter range the differential mobility becomes negative, and b) the
biased particle drives the whole system into a nonequilibrium steady-state with
a stationary particle density profile past the tracer, which decays
exponentially, in sharp contrast with the behavior observed for unbounded
lattices, where an algebraic decay is known to take place. | cond-mat_stat-mech |
Describing the ground state of quantum systems through statistical
mechanics: We present a statistical mechanics description to study the ground state of
quantum systems. In this approach, averages for the complete system are
calculated over the non-interacting energy levels. Taking different interaction
parameter, the particles of the system fall into non-interacting microstates,
corresponding to different occupation probabilities for these energy levels.
Using this novel thermodynamic interpretation we study the Hubbard model for
the case of two electrons in two sites and for the half-filled band on a
one-dimensional lattice. We show that the form of the entropy depends on the
specific system considered. | cond-mat_stat-mech |
The Boltzmann temperature and Lagrange multiplier: We consider the relation between the Boltzmann temperature and the Lagrange
multipliers associated with energy average in the nonextensive
thermostatistics. In Tsallis' canonical ensemble, the Boltzmann temperature
depends on energy through the probability distribution unless $q=1$. It is
shown that the so-called 'physical temperature' introduced in [Phys. Lett. A
\textbf{281} (2001) 126] is nothing but the ensemble average of the Boltzmann
temperature. | cond-mat_stat-mech |
Glassy behaviour in an exactly solved spin system with a ferromagnetic
transition: We show that applying simple dynamical rules to Baxter's eight-vertex model
leads to a system which resembles a glass-forming liquid. There are analogies
with liquid, supercooled liquid, glassy and crystalline states. The disordered
phases exhibit strong dynamical heterogeneity at low temperatures, which may be
described in terms of an emergent mobility field. Their dynamics are
well-described by a simple model with trivial thermodynamics, but an emergent
kinetic constraint. We show that the (second order) thermodynamic transition to
the ordered phase may be interpreted in terms of confinement of the excitations
in the mobility field. We also describe the aging of disordered states towards
the ordered phase, in terms of simple rate equations. | cond-mat_stat-mech |
Equilibrium Microcanonical Annealing for First-Order Phase Transitions: A framework is presented for carrying out simulations of equilibrium systems
in the microcanonical ensemble using annealing in an energy ceiling. The
framework encompasses an equilibrium version of simulated annealing, population
annealing and hybrid algorithms that interpolate between these extremes. These
equilibrium, microcanonical annealing algorithms are applied to the thermal
first-order transition in the 20-state, two-dimensional Potts model. All of
these algorithms are observed to perform well at the first-order transition
though for the system sizes studied here, equilibrium simulated annealing is
most efficient. | cond-mat_stat-mech |
High Precision Fourier Monte Carlo Simulation of Crystalline Membranes: We report an essential improvement of the plain Fourier Monte Carlo algorithm
that promises to be a powerful tool for investigating critical behavior in a
large class of lattice models, in particular those containing microscopic or
effective long-ranged interactions. On tuning the Monte Carlo acceptance rates
separately for each wave vector, we are able to drastically reduce critical
slowing down. We illustrate the resulting efficiency and unprecedented accuracy
of our algorithm with a calculation of the universal elastic properties of
crystalline membranes in the flat phase and derive a numerical estimate eta =
0.795(10) for the critical exponent eta that challenges those derived from
other recent simulations. The large system sizes accessible to our present
algorithm also allow to demonstrate that insufficiently taking into account
corrections to scaling may severely hamper a finite size scaling analysis. This
observation may also help to clarify the apparent disagreement of published
numerical estimates of eta in the existing literature. | cond-mat_stat-mech |
Boundary drive induced formation of aggregate condensates in stochastic
transport with short-range interactions: We discuss the effects of particle exchange through open boundaries and the
induced drive on the phase structure and condensation phenomena of a stochastic
transport process with tunable short-range interactions featuring
pair-factorized steady states (PFSS) in the closed system. In this model, the
steady state of the particle hopping process can be tuned to yield properties
from the zero-range process (ZRP) condensation model to those of models with
spa- tially extended condensates. By varying the particle exchange rates as
well as the presence of a global drift, we observe a phase transition from a
free particle gas to a phase with condensates aggregated to the boundaries.
While this transition is similar to previous results for the ZRP, we find that
the mechanism is different as the presence of the boundary actually influences
the interaction due to the non-zero interaction range. | cond-mat_stat-mech |
Granular gas of viscoelastic particles in a homogeneous cooling state: Kinetic properties of a granular gas of viscoelastic particles in a
homogeneous cooling state are studied analytically and numerically. We employ
the most recent expression for the velocity-dependent restitution coefficient
for colliding viscoelastic particles, which allows to describe systems with
large inelasticity. In contrast to previous studies, the third coefficient a3
of the Sonine polynomials expansion of the velocity distribution function is
taken into account. We observe a complicated evolution of this coefficient.
Moreover, we find that a3 is always of the same order of magnitude as the
leading second Sonine coefficient a2; this contradicts the existing hypothesis
that the subsequent Sonine coefficients a2, a3 ..., are of an ascending order
of a small parameter, characterizing particles inelasticity. We analyze
evolution of the high-energy tail of the velocity distribution function. In
particular, we study the time dependence of the tail amplitude and of the
threshold velocity, which demarcates the main part of the velocity distribution
and the high-energy part. We also study evolution of the self-diffusion
coefficient D and explore the impact of the third Sonine coefficient on the
self-diffusion. Our analytical predictions for the third Sonine coefficient,
threshold velocity and the self-diffusion coefficient are in a good agreement
with the numerical finding. | cond-mat_stat-mech |
Power-law distributions for the areas of the basins of attraction on a
potential energy landscape: Energy landscape approaches have become increasingly popular for analysing a
wide variety of chemical physics phenomena. Basic to many of these applications
has been the inherent structure mapping, which divides up the potential energy
landscape into basins of attraction surrounding the minima. Here, we probe the
nature of this division by introducing a method to compute the basin area
distribution and applying it to some archetypal supercooled liquids. We find
that this probability distribution is a power law over a large number of
decades with the lower-energy minima having larger basins of attraction.
Interestingly, the exponent for this power law is approximately the same as
that for a high-dimensional Apollonian packing, providing further support for
the suggestion that there is a strong analogy between the way the energy
landscape is divided into basins, and the way that space is packed in
self-similar, space-filling hypersphere packings, such as the Apollonian
packing. These results suggest that the basins of attraction provide a
fractal-like tiling of the energy landscape, and that a scale-free pattern of
connections between the minima is a general property of energy landscapes. | cond-mat_stat-mech |
Force fluctuation in a driven elastic chain: We study the dynamics of an elastic chain driven on a disordered substrate
and analyze numerically the statistics of force fluctuations at the depinning
transition. The probability distribution function of the amplitude of the slip
events for small velocities is a power law with an exponent $+AFw-tau$
depending on the driving velocity. This result is in qualitative agreement with
experimental measurements performed on sliding elastic surfaces with
macroscopic asperities. We explore the properties of the depinning transition
as a function of the driving mode (i.e. constant force or constant velocity)
and compute the force-velocity diagram using finite size scaling methods. The
scaling exponents are in excellent agreement with the values expected in
interface models and, contrary to previous studies, we found no difference in
the exponents for periodic and disordered chains. | cond-mat_stat-mech |
Binary data corruption due to a Brownian agent II: two dimensions,
competing agents, and generalized couplings: This work is a continuation of our previous investigation of binary data
corruption due to a Brownian agent [T. J. Newman and W. Triampo, preprint
cond-mat/9811237]. We extend our study in three main directions which allow us
to make closer contact with real bistable systems. These are i) a detailed
analysis of two dimensions, ii) the case of competing agents, and iii) the
cases of asymmetric and quenched random couplings. Most of our results are
obtained by extending our original phenomenological model, and are supported by
extensive numerical simulations. | cond-mat_stat-mech |
Dynamics of collapsing and exploding Bose-Einstein condensates: We explored the dynamics of how a Bose-Einstein condensate collapses and
subsequently explodes when the balance of forces governing the size and shape
of the condensate is suddenly altered. A condensate's equilibrium size and
shape is strongly affected by the inter-atomic interactions. Our ability to
induce a collapse by switching the interactions from repulsive to attractive by
tuning an externally-applied magnetic field yields a wealth of detailed
information on the violent collapse process. We observe anisotropic atom bursts
that explode from the condensate, atoms leaving the condensate in undetected
forms, spikes appearing in the condensate wave function, and oscillating
remnant condensates that survive the collapse. These all have curious
dependencies on time, the strength of the interaction, and the number of
condensate atoms. Although ours would seem to be a simple well-characterized
system, our measurements reveal many interesting phenomena that challenge
theoretical models. | cond-mat_stat-mech |
Consistent description of kinetics and hydrodynamics of dusty plasma: A consistent statistical description of kinetics and hydrodynamics of dusty
plasma is proposed based on the Zubarev nonequilibrium statistical operator
method. For the case of partial dynamics the nonequilibrium statistical
operator and the generalized transport equations for a consistent description
of kinetics of dust particles and hydrodynamics of electrons, ions and neutral
atoms are obtained. In the approximation of weakly nonequilibrium process a
spectrum of collective excitations of dusty plasma is investigated in the
hydrodynamic limit. | cond-mat_stat-mech |
Metastability in the Hamiltonian Mean Field model and Kuramoto model: We briefly discuss the state of the art on the anomalous dynamics of the
Hamiltonian Mean Field model. We stress the important role of the initial
conditions for understanding the microscopic nature of the intriguing
metastable quasi stationary states observed in the model and the connections to
Tsallis statistics and glassy dynamics. We also present new results on the
existence of metastable states in the Kuramoto model and discuss the
similarities with those found in the HMF model. The existence of metastability
seem to be quite a common phenomenon in fully coupled systems, whose origin
could be also interpreted as a dynamical mechanism preventing or hindering
sinchronization. | cond-mat_stat-mech |
Effect of Constraint Relaxation on the Minimum Vertex Cover Problem in
Random Graphs: A statistical-mechanical study of the effect of constraint relaxation on the
minimum vertex cover problem in Erd\H{o}s-R\'enyi random graphs is presented.
Using a penalty-method formulation for constraint relaxation, typical
properties of solutions, including infeasible solutions that violate the
constraints, are analyzed by means of the replica method and cavity method. The
problem involves a competition between reducing the number of vertices to be
covered and satisfying the edge constraints. The analysis under the
replica-symmetric (RS) ansatz clarifies that the competition leads to
degeneracies in the vertex and edge states, which determine the quantitative
properties of the system, such as the cover and penalty ratios. A precise
analysis of these effects improves the accuracy of RS approximation for the
minimum cover ratio in the replica symmetry breaking (RSB) region. Furthermore,
the analysis based on the RS cavity method indicates that the RS/RSB boundary
of the ground states with respect to the mean degree of the graphs is expanded,
and the critical temperature is lowered by constraint relaxation. | cond-mat_stat-mech |
Fermionic R-operator approach for the small-polaron model with open
boundary condition: Exact integrability and algebraic Bethe ansatz of the small-polaron model
with the open boundary condition are discussed in the framework of the quantum
inverse scattering method (QISM). We employ a new approach where the fermionic
R-operator which consists of fermion operators is a key object. It satisfies
the Yang-Baxter equation and the reflection equation with its corresponding
K-operator. Two kinds of 'super-transposition' for the fermion operators are
defined and the dual reflection equation is obtained. These equations prove the
integrability and the Bethe ansatz equation which agrees with the one obtained
from the graded Yang-Baxter equation and the graded reflection equations. | cond-mat_stat-mech |
Exact relaxation in a class of non-equilibrium quantum lattice systems: A reasonable physical intuition in the study of interacting quantum systems
says that, independent of the initial state, the system will tend to
equilibrate. In this work we study a setting where relaxation to a steady state
is exact, namely for the Bose-Hubbard model where the system is quenched from a
Mott quantum phase to the strong superfluid regime. We find that the evolving
state locally relaxes to a steady state with maximum entropy constrained by
second moments, maximizing the entanglement, to a state which is different from
the thermal state of the new Hamiltonian. Remarkably, in the infinite system
limit this relaxation is true for all large times, and no time average is
necessary. For large but finite system size we give a time interval for which
the system locally "looks relaxed" up to a prescribed error. Our argument
includes a central limit theorem for harmonic systems and exploits the finite
speed of sound. Additionally, we show that for all periodic initial
configurations, reminiscent of charge density waves, the system relaxes
locally. We sketch experimentally accessible signatures in optical lattices as
well as implications for the foundations of quantum statistical mechanics. | cond-mat_stat-mech |
Self-Consistent Theory of Rupture by Progressive Diffuse Damage: We analyze a self-consistent theory of crack growth controlled by a
cumulative damage variable d(t) dependent on stress history. As a function of
the damage exponent $m$, which controls the rate of damage dd/dt \propto
sigma^m as a function of local stress $\sigma$, we find two regimes. For 0 < m
< 2, the model predicts a finite-time singularity. This retrieves previous
results by Zobnin for m=1 and by Bradley and Wu for 0 < m < 2. To improve on
this self-consistent theory which neglects the dependence of stress on damage,
we apply the functional renormalization method of Yukalov and Gluzman and find
that divergences are replaced by singularities with exponents in agreement with
those found in acoustic emission experiments. For m =2 and m > 2, the rupture
dynamics is not defined without the introduction of a regularizing scheme. We
investigate three regularization schemes involving respectively a saturation of
damage, a minimum distance of approach to the crack tip and a fixed stress
maximum. In the first and third schemes, the finite-time singularity is
replaced by a crack dynamics defined for all times but which is controlled by
either the existence of a microscopic scale at which the stress is regularized
or by the maximum sustainable stress. In the second scheme, a finite-time
singularity is again found. In the first two schemes within this regime m > 2,
the theory has no continuous limit. | cond-mat_stat-mech |
Accurate Estimation of Diffusion Coefficients and their Uncertainties
from Computer Simulation: Self-diffusion coefficients, $D^*$, are routinely estimated from molecular
dynamics simulations by fitting a linear model to the observed mean-squared
displacements (MSDs) of mobile species. MSDs derived from simulation suffer
from statistical noise, which introduces uncertainty in the resulting estimate
of $D^*$. An optimal scheme for estimating $D^*$ will minimise this
uncertainty, i.e., will have high statistical efficiency, and will give an
accurate estimate of the uncertainty itself. We present a scheme for estimating
$D^*$ from a single simulation trajectory with high statistical efficiency and
accurately estimating the uncertainty in the predicted value. The statistical
distribution of MSDs observable from a given simulation is modelled as a
multivariate normal distribution using an analytical covariance matrix for an
equivalent system of freely diffusing particles, which we parameterise from the
available simulation data. We then perform Bayesian regression to sample the
distribution of linear models that are compatible with this model multivariate
normal distribution, to obtain a statistically efficient estimate of $D^*$ and
an accurate estimate of the associated statistical uncertainty. | cond-mat_stat-mech |
Derivation of the percolation threshold for the network model of
Barabasi and Albert: The percolation threshold of the network model by Barabasi and Albert
(BA-model) [Science 286, 509 (1999)] has thus far only been 'guessed' based on
simulations and comparison with other models. Due to the still uncertain
influence of correlations, the reference to other models cannot be justified.
In this paper, we explicitly derive the well-known values for the BA-model. To
underline the importance of a null model like that of Barabasi and Albert, we
close with two basic remarks. First, we establish a connection between the
abundance of scale-free networks in nature and the fact that power-law tails in
the degree distribution result only from (at least asymptotically) linear
preferential attachment: Only in the case of linear preferential attachment
does a minimum of topological knowledge about the network suffice for the
attachment process. Second, we propose a very simple and realistic extension of
the BA-model that accounts for clustering. We discuss the influence of
clustering on the percolation properties. | cond-mat_stat-mech |
Towards entanglement negativity of two disjoint intervals for a one
dimensional free fermion: We study the moments of the partial transpose of the reduced density matrix
of two intervals for the free massless Dirac fermion. By means of a direct
calculation based on coherent state path integral, we find an analytic form for
these moments in terms of the Riemann theta function. We show that the moments
of arbitrary order are equal to the same quantities for the compactified boson
at the self-dual point. These equalities imply the non trivial result that also
the negativity of the free fermion and the self-dual boson are equal. | cond-mat_stat-mech |
Percolation approach to glassy dynamics with continuously broken
ergodicity: We show that the relaxation dynamics near a glass transition with continuous
ergodicity breaking can be endowed with a geometric interpretation based on
percolation theory. At mean-field level this approach is consistent with the
mode-coupling theory (MCT) of type-A liquid-glass transitions and allows to
disentangle the universal and nonuniversal contributions to MCT relaxation
exponents. Scaling predictions for the time correlation function are
successfully tested in the F12 schematic model and facilitated spin systems on
a Bethe lattice. Our approach immediately suggests the extension of MCT scaling
laws to finite spatial dimensions and yields new predictions for dynamic
relaxation exponents below an upper critical dimension of 6. | cond-mat_stat-mech |
Brownian motion under annihilation dynamics: The behavior of a heavy tagged intruder immersed in a bath of particles
evolving under ballistic annihilation dynamics is investigated. The
Fokker-Planck equation for this system is derived and the peculiarities of the
corresponding diffusive behavior are worked out. In the long time limit, the
intruder velocity distribution function approaches a Gaussian form, but with a
different temperature from its bath counterpart. As a consequence of the
continuous decay of particles in the bath, the mean squared displacement
increases exponentially in the collision per particle time scale. Analytical
results are finally successfully tested against Monte Carlo numerical
simulations. | cond-mat_stat-mech |
An exact solution to asymptotic Bethe equation: We present an exact solution to the asymptotic Bethe equation of weakly
anisotropic Heisenberg spin chain, which is a set of non-linear algebraic
equations. The solution describes the low-energy excitations above
ferromagnetic ground state with fixed magnetisation, and it has a close
relation to generalised Jacobi polynomial. It is equivalent to a generalised
Stieltjes problem and in the continuous limit, it becomes a Riemann-Hilbert
problem closely related to the finite-gap solutions of classical
Landau-Lifshitz field theory. | cond-mat_stat-mech |
Correlation function structure in square-gradient models of the
liquid-gas interface: Exact results and reliable approximations: In a recent article, we described how the microscopic structure of
density-density correlations in the fluid interfacial region, for systems with
short-ranged forces, can be understood by considering the resonances of the
local structure factor occurring at specific parallel wave-vectors $q$. Here,
we investigate this further by comparing approximations for the local structure
factor and correlation function against three new examples of analytically
solvable models within square-gradient theory. Our analysis further
demonstrates that these approximations describe the correlation function and
structure factor across the whole spectrum of wave-vectors, encapsulating the
cross-over from the Goldstone mode divergence (at small $q$) to bulk-like
behaviour (at larger $q$). As shown, these approximations are exact for some
square-gradient model potentials, and never more than a few percent inaccurate
for the others. Additionally, we show that they very accurately describe the
correlation function structure for a model describing an interface near a
tricritical point. In this case, there are no analytical solutions for the
correlation functions, but the approximations are near indistinguishable from
the numerical solutions of the Ornstein-Zernike equation. | cond-mat_stat-mech |
Entanglement Spectra and Entanglement Thermodynamics of Hofstadter
Bilayers: We study Hofstadter bilayers, i.e. coupled hopping models on two-dimensional
square lattices in a perpendicular magnetic field. Upon tracing out one of the
layers, we find an explicit expression for the resulting entanglement spectrum
in terms of the energy eigenvalues of the underlying monolayer system. For
strongly coupled layers the entanglement Hamiltonian is proportional to the
energetic Hamiltonian of the monolayer system. The proportionality factor,
however, cannot be interpreted as the inverse thermodynamic temperature, but
represents a phenomenological temperature scale. We derive an explicit relation
between both temperature scales which is in close analogy to a standard result
of classic thermodynamics. In the limit of vanishing temperature, thermodynamic
quantities such as entropy and inner energy approach their ground-state values,
but show a fractal structure as a function of magnetic flux. | cond-mat_stat-mech |
Numerical exploration of the Aging effects in spin systems: An interesting concept that has been underexplored in the context of
time-dependent simulations is the correlation of total magnetization, $C(t)$%.
One of its main advantages over directly studying magnetization is that we do
not need to meticulously prepare initial magnetizations. This is because the
evolutions are computed from initial states with spins that are independent and
completely random. In this paper, we take an important step in demonstrating
that even for time evolutions from other initial conditions, $C(t_{0},t)$, a
suitable scaling can be performed to obtain universal power laws. We
specifically consider the significant role played by the second moment of
magnetization. Additionally, we complement the study by conducting a recent
investigation of random matrices, which are applied to determine the critical
properties of the system. Our results show that the aging in the time series of
magnetization influences the spectral properties of matrices and their ability
to determine the critical temperature of systems. | cond-mat_stat-mech |
Universal Order and Gap Statistics of Critical Branching Brownian Motion: We study the order statistics of one dimensional branching Brownian motion in
which particles either diffuse (with diffusion constant $D$), die (with rate
$d$) or split into two particles (with rate $b$). At the critical point $b=d$
which we focus on, we show that, at large time $t$, the particles are
collectively bunched together. We find indeed that there are two length scales
in the system: (i) the diffusive length scale $\sim \sqrt{Dt}$ which controls
the collective fluctuations of the whole bunch and (ii) the length scale of the
gap between the bunched particles $\sim \sqrt{D/b}$. We compute the probability
distribution function $P(g_k,t|n)$ of the $k$th gap $g_k = x_k - x_{k+1}$
between the $k$th and $(k+1)$th particles given that the system contains
exactly $n>k$ particles at time $t$. We show that at large $t$, it converges to
a stationary distribution $P(g_k,t\to \infty|n) = p(g_k|n)$ with an algebraic
tail $p(g_k|n) \sim 8(D/b) g_k^{-3}$, for $g_k \gg 1$, independent of $k$ and
$n$. We verify our predictions with Monte Carlo simulations. | cond-mat_stat-mech |
Effective Floquet-Gibbs states for dissipative quantum systems: A periodically driven quantum system, when coupled to a heat bath, relaxes to
a non-equilibrium asymptotic state. In the general situation, the retrieval of
this asymptotic state presents a rather non-trivial task. It was recently shown
that in the limit of an infinitesimal coupling, using so-called rotating wave
approximation (RWA), and under strict conditions imposed on the time-dependent
system Hamiltonian, the asymptotic state can attain the Gibbs form. A
Floquet-Gibbs state is characterized by a density matrix which is diagonal in
the Floquet basis of the system Hamiltonian with the diagonal elements obeying
a Gibbs distribution, being parametrized by the corresponding Floquet
quasi-energies. Addressing the non-adiabatic driving regime, upon using the
Magnus expansion, we employ the concept of a corresponding effective Floquet
Hamiltonian. In doing so we go beyond the conventionally used RWA and
demonstrate that the idea of Floquet-Gibbs states can be extended to the
realistic case of a weak, although finite system-bath coupling, herein termed
effective Floquet-Gibbs states. | cond-mat_stat-mech |
Prediction, Retrodiction, and The Amount of Information Stored in the
Present: We introduce an ambidextrous view of stochastic dynamical systems, comparing
their forward-time and reverse-time representations and then integrating them
into a single time-symmetric representation. The perspective is useful
theoretically, computationally, and conceptually. Mathematically, we prove that
the excess entropy--a familiar measure of organization in complex systems--is
the mutual information not only between the past and future, but also between
the predictive and retrodictive causal states. Practically, we exploit the
connection between prediction and retrodiction to directly calculate the excess
entropy. Conceptually, these lead one to discover new system invariants for
stochastic dynamical systems: crypticity (information accessibility) and causal
irreversibility. Ultimately, we introduce a time-symmetric representation that
unifies all these quantities, compressing the two directional representations
into one. The resulting compression offers a new conception of the amount of
information stored in the present. | cond-mat_stat-mech |
Optimal Work Extraction and the Minimum Description Length Principle: We discuss work extraction from classical information engines (e.g.,
Szil\'ard) with $N$-particles, $q$ partitions, and initial arbitrary
non-equilibrium states. In particular, we focus on their {\em optimal}
behaviour, which includes the measurement of a set of quantities $\Phi$ with a
feedback protocol that extracts the maximal average amount of work. We show
that the optimal non-equilibrium state to which the engine should be driven
before the measurement is given by the normalised maximum-likelihood
probability distribution of a statistical model that admits $\Phi$ as
sufficient statistics. Furthermore, we show that the minimax universal code
redundancy $\mathcal{R}^*$ associated to this model, provides an upper bound to
the work that the demon can extract on average from the cycle, in units of
$k_{\rm B}T$. We also find that, in the limit of $N$ large, the maximum average
extracted work cannot exceed $H[\Phi]/2$, i.e. one half times the Shannon
entropy of the measurement. Our results establish a connection between optimal
work extraction in stochastic thermodynamics and optimal universal data
compression, providing design principles for optimal information engines. In
particular, they suggest that: (i) optimal coding is thermodynamically
efficient, and (ii) it is essential to drive the system into a critical state
in order to achieve optimal performance. | cond-mat_stat-mech |
Non-KPZ modes in two-species driven diffusive systems: Using mode coupling theory and dynamical Monte-Carlo simulations we
investigate the scaling behaviour of the dynamical structure function of a
two-species asymmetric simple exclusion process, consisting of two coupled
single-lane asymmetric simple exclusion processes. We demonstrate the
appearence of a superdiffusive mode with dynamical exponent $z=5/3$ in the
density fluctuations, along with a KPZ mode with $z=3/2$ and argue that this
phenomenon is generic for short-ranged driven diffusive systems with more than
one conserved density. When the dynamics is symmetric under the interchange of
the two lanes a diffusive mode with $z=2$ appears instead of the non-KPZ
superdiffusive mode. | cond-mat_stat-mech |
A fluctuation relation for weakly ergodic aging systems: A fluctuation relation for aging systems is introduced, and verified by
extensive numerical simulations. It is based on the hypothesis of partial
equilibration over phase space regions in a scenario of entropy-driven
relaxation. The relation provides a simple alternative method, amenable of
experimental implementation, to measure replica symmetry breaking parameters in
aging systems. The connection with the effective temperatures obtained from the
fluctuation-dissipation theorem is discussed. | cond-mat_stat-mech |
Stationary behaviour of observables after a quantum quench in the
spin-1/2 Heisenberg XXZ chain: We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late
times after the quench it is believed that the expectation values of local
operators approach time-independent values, that are described by a generalized
Gibbs ensemble. Employing a quantum transfer matrix approach we show how to
determine short-range correlation functions in such generalized Gibbs ensembles
for a class of initial states. | cond-mat_stat-mech |
Magnetic Properties of the Metamagnet Ising Model in a three-dimensional
Lattice in a Random and Uniform Field: By employing the Monte Carlo technique we study the behavior of Metamagnet
Ising Model in a random field. The phase diagram is obtained by using the
algorithm of Glaubr in a cubic lattice of linear size $L$ with values ranging
from 16 to 42 and with periodic boundary conditions. | cond-mat_stat-mech |
Prethermalization in periodically-driven nonreciprocal many-body spin
systems: We analyze a new class of time-periodic nonreciprocal dynamics in interacting
chaotic classical spin systems, whose equations of motion are conservative
(phase-space-volume-preserving) yet possess no symplectic structure. As a
result, the dynamics of the system cannot be derived from any time-dependent
Hamiltonian. In the high-frequency limit, we find that the magnetization
dynamics features a long-lived metastable plateau, whose duration is controlled
by the fourth power of the drive frequency. However, due to the lack of an
effective Hamiltonian, the prethermal state the system evolves into cannot be
understood within the framework of the canonical ensemble. We propose a
Hamiltonian extension of the system using auxiliary degrees of freedom, in
which the original spins constitute an open yet nondissipative subsystem. This
allows us to perturbatively derive effective equations of motion that
manifestly display symplecticity breaking at leading order in the inverse
frequency. We thus extend the notion of prethermal dynamics, observed in the
high-frequency limit of periodically-driven systems, to nonreciprocal systems. | cond-mat_stat-mech |
Giant leaps and long excursions: fluctuation mechanisms in systems with
long-range memory: We analyse large deviations of time-averaged quantities in stochastic
processes with long-range memory, where the dynamics at time t depends itself
on the value q_t of the time-averaged quantity. First we consider the elephant
random walk and a Gaussian variant of this model, identifying two mechanisms
for unusual fluctuation behaviour, which differ from the Markovian case. In
particular, the memory can lead to large deviation principles with reduced
speeds, and to non-analytic rate functions. We then explain how the mechanisms
operating in these two models are generic for memory-dependent dynamics and
show other examples including a non-Markovian symmetric exclusion process. | cond-mat_stat-mech |
Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian
Noise: For a wide class of stochastic athermal systems, we derive Langevin-like
equations driven by non-Gaussian noise, starting from master equations and
developing a new asymptotic expansion. We found an explicit condition whereby
the non-Gaussian properties of the athermal noise become dominant for tracer
particles associated with both thermal and athermal environments. Furthermore,
we derive an inverse formula to infer microscopic properties of the athermal
bath from the statistics of the tracer particle. We apply our formulation to a
granular motor under viscous friction, and analytically obtain the angular
velocity distribution function. Our theory demonstrates that the non-Gaussian
Langevin equation is the minimal model of athermal systems. | cond-mat_stat-mech |
Magnetization Transfer by a Quantum Ring Device: We show that a tight-binding model device consisting of a laterally connected
ring at half filling in a tangent time-dependent magnetic field can in
principle be designed to pump a purely spin current. The process exploits the
spin-orbit interaction in the ring. This behavior is understood analytically
and found to be robust with respect to temperature and small deviations from
half filling. | cond-mat_stat-mech |
Noise influence on solid-liquid transition of ultrathin lubricant film: The melting of ultrathin lubricant film by friction between atomically flat
surfaces is studied. The additive noises of the elastic shear stress and
strain, and the temperature are introduced for building a phase diagram with
the domains of sliding, stick-slip, and dry friction. It is shown that increase
of the strain noise intensity causes the lubricant film melting even at low
temperatures of the friction surfaces. | cond-mat_stat-mech |
Strong-coupling critical behavior in three-dimensional lattice Abelian
gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry: We consider a three-dimensional lattice Abelian Higgs gauge model for a
charged $N$-component scalar field ${\phi}$, which is invariant under $SO(N)$
global transformations for generic values of the parameters. We focus on the
strong-coupling regime, in which the kinetic Hamiltonian term for the gauge
field is a small perturbation, which is irrelevant for the critical behavior.
The Hamiltonian depends on a parameter $v$ which determines the global symmetry
of the model and the symmetry of the low-temperature phases. We present
renormalization-group predictions, based on a Landau-Ginzburg-Wilson effective
description that relies on the identification of the appropriate order
parameter and on the symmetry-breaking patterns that occur at the
strong-coupling phase transitions. For $v=0$, the global symmetry group of the
model is $SU(N)$; the corresponding model may undergo continuous transitions
only for $N=2$. For $v\not=0$, i.e., in the $SO(N)$ symmetric case, continuous
transitions (in the Heisenberg universality class) are possible also for $N=3$
and 4. We perform Monte Carlo simulations for $N=2,3,4,6$, to verify the
renormalization-group predictions. Finite-size scaling analyses of the
numerical data are in full agreement. | cond-mat_stat-mech |
Thermodynamic Geometry, Phase Transitions, and the Widom Line: We construct a novel approach, based on thermodynamic geometry, to
characterize first-order phase transitions from a microscopic perspective,
through the scalar curvature in the equilibrium thermodynamic state space. Our
method resolves key theoretical issues in macroscopic thermodynamic constructs,
and furthermore characterizes the Widom line through the maxima of the
correlation length, which is captured by the thermodynamic scalar curvature. As
an illustration of our method, we use it in conjunction with the mean field Van
der Waals equation of state to predict the coexistence curve and the Widom
line. Where closely applicable, it provides excellent agreement with
experimental data. The universality of our method is indicated by direct
calculations from the NIST database. | cond-mat_stat-mech |
Local pressure of confined fluids inside nanoslit pores -- A density
functional theory prediction: In this work, the local pressure of fluids confined inside nanoslit pores is
predicted within the framework of the density functional theory. The
Euler-Lagrange equation in the density functional theory of statistical
mechanics is used to obtain the force balance equation which leads to a general
equation to predict the local normal component of the pressure tensor. Our
approach yields a general equation for predicting the normal pressure of
confined fluids and it satisfies the exact bulk thermodynamics equation when
the pore width approaches infinity. As two basic examples, we report the
solution of the general equation for hard-sphere (HS) and Lennard-Jones (LJ)
fluids confined between two parallel-structureless hard walls. To do so, we use
the modified fundamental measure theory (mFMT) to obtain the normal pressure
for hard-sphere confined fluid and mFMT incorporated with the Rosenfeld
perturbative DFT for the LJ fluid. Effects of different variables including
pore width, bulk density and temperature on the behavior of normal pressure are
studied and reported. Our predicted results show that in both HS and LJ cases
the confined fluids normal pressure has an oscillatory behavior and the number
of oscillations increases with bulk density and temperature. The oscillations
also become broad and smooth with pore width at a constant temperature and bulk
density. In comparison with the HS confined fluid, the values of normal
pressure for the LJ confined fluid as well as its oscillations at all distances
from the walls are less profound. | cond-mat_stat-mech |
Nonextensive Entropy, Prior PDFs and Spontaneous Symmetry Breaking: We show that using nonextensive entropy can lead to spontaneous symmetry
breaking when a parameter changes its value from that applicable for a
symmetric domain, as in field theory. We give the physical reasons and also
show that even for symmetric Dirichlet priors, such a defnition of the entropy
and the parameter value can lead to asymmetry when entropy is maximized. | cond-mat_stat-mech |
Cardy's Formula for some Dependent Percolation Models: We prove Cardy's formula for rectangular crossing probabilities in dependent
site percolation models that arise from a deterministic cellular automaton with
a random initial state. The cellular automaton corresponds to the
zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal
lattice H (with alternating updates of two sublattices); it may also be
realized on the triangular lattice T with flips when a site disagrees with six,
five and sometimes four of its six neighbors. | cond-mat_stat-mech |
The delayed uncoupled continuous-time random walks do not provide a
model for the telegraph equation: It has been alleged in several papers that the so called delayed
continuous-time random walks (DCTRWs) provide a model for the one-dimensional
telegraph equation at microscopic level. This conclusion, being widespread now,
is strange, since the telegraph equation describes phenomena with finite
propagation speed, while the velocity of the motion of particles in the DCTRWs
is infinite. In this paper we investigate how accurate are the approximations
to the DCTRWs provided by the telegraph equation. We show that the diffusion
equation, being the correct limit of the DCTRWs, gives better approximations in
$L_2$ norm to the DCTRWs than the telegraph equation. We conclude therefore
that, first, the DCTRWs do not provide any correct microscopic interpretation
of the one-dimensional telegraph equation, and second, the kinetic (exact)
model of the telegraph equation is different from the model based on the
DCTRWs. | cond-mat_stat-mech |
Understanding the phenomenon of viscous slowing down of glass-forming
liquids from the static pair correlation function: A theory which uses data of the static pair-correlation function is developed
to calculate quantities associated with the viscous slowing down of supercooled
liquids. We calculate value of the energy fluctuations that determine the
number of stable bonds a particle forms with neighbors from data of the
structural relaxation time. The number of bonds and the activation energy for
relaxation are shown to increase sharply in a narrow temperature range close to
the glass temperature. The configurational entropy calculated from values of
the configurational fluctuations is found in good agreement with the value
determined from simulations. | cond-mat_stat-mech |
Finite-temperature quantum discordant criticality: In quantum statistical mechanics, finite-temperature phase transitions are
typically governed by classical field theories. In this context, the role of
quantum correlations is unclear: recent contributions have shown how
entanglement is typically very short-ranged, and thus uninformative about
long-ranged critical correlations. In this work, we show the existence of
finite-temperature phase transitions where a broader form of quantum
correlation than entanglement, the entropic quantum discord, can display
genuine signatures of critical behavior. We consider integrable bosonic field
theories in both two- and three-dimensional lattices, and show how the two-mode
Gaussian discord decays algebraically with the distance even in cases where the
entanglement negativity vanishes beyond nearest-neighbor separations.
Systematically approaching the zero-temperature limit allows us to connect
discord to entanglement, drawing a generic picture of quantum correlations and
critical behavior that naturally describes the transition between entangled and
discordant quantum matter. | cond-mat_stat-mech |
Computing phase diagrams for a quasicrystal-forming patchy-particle
system: We introduce an approach to computing the free energy of quasicrystals, which
we use to calculate phase diagrams for systems of two-dimensional patchy
particles with five regularly arranged patches that have previously been shown
to form dodecagonal quasicrystals. We find that the quasicrystal is a
thermodynamically stable phase for a wide range of conditions and remains a
robust feature of the system as the potential's parameters are varied. We also
demonstrate that the quasicrystal is entropically stabilised over its
crystalline approximants. | cond-mat_stat-mech |
Heaps' law, statistics of shared components and temporal patterns from a
sample-space-reducing process: Zipf's law is a hallmark of several complex systems with a modular structure,
such as books composed by words or genomes composed by genes. In these
component systems, Zipf's law describes the empirical power law distribution of
component frequencies. Stochastic processes based on a sample-space-reducing
(SSR) mechanism, in which the number of accessible states reduces as the system
evolves, have been recently proposed as a simple explanation for the ubiquitous
emergence of this law. However, many complex component systems are
characterized by other statistical patterns beyond Zipf's law, such as a
sublinear growth of the component vocabulary with the system size, known as
Heap's law, and a specific statistics of shared components. This work shows,
with analytical calculations and simulations, that these statistical properties
can emerge jointly from a SSR mechanism, thus making it an appropriate
parameter-poor representation for component systems. Several alternative (and
equally simple) models, for example based on the preferential attachment
mechanism, can also reproduce Heaps' and Zipf's laws, suggesting that
additional statistical properties should be taken into account to select the
most-likely generative process for a specific system. Along this line, we will
show that the temporal component distribution predicted by the SSR model is
markedly different from the one emerging from the popular rich-gets-richer
mechanism. A comparison with empirical data from natural language indicates
that the SSR process can be chosen as a better candidate model for text
generation based on this statistical property. Finally, a limitation of the SSR
model in reproducing the empirical "burstiness" of word appearances in texts
will be pointed out, thus indicating a possible direction for extensions of the
basic SSR process. | cond-mat_stat-mech |
Differences between regular and random order of updates in damage
spreading simulations: We investigate the spreading of damage in the three-dimensional Ising model
by means of large-scale Monte-Carlo simulations. Within the Glauber dynamics we
use different rules for the order in which the sites are updated. We find that
the stationary damage values and the spreading temperature are different for
different update order. In particular, random update order leads to larger
damage and a lower spreading temperature than regular order. Consequently,
damage spreading in the Ising model is non-universal not only with respect to
different update algorithms (e.g. Glauber vs. heat-bath dynamics) as already
known, but even with respect to the order of sites. | cond-mat_stat-mech |
Power-law behaviors from the two-variable Langevin equation: Ito's and
Stratonovich's Fokker-Planck equations: We study power-law behaviors produced from the stochastically dynamical
system governed by the well-known two-variable Langevin equations. The
stationary solutions of the corresponding Ito's, Stratonovich's and the
Zwanzig's (the backward Ito's) Fokker-Planck equations are solved under a new
fluctuation-dissipation relation, which are presented in a unified form of the
power-law distributions with a power index containing two parameter kappa and
sigma, where kappa measures a distance away from the thermal equilibrium and
sigma distinguishes the above three forms of the Fokker-Planck equations. The
numerical calculations show that the Ito's, the Stratonovich's and the
Zwanzig's form of the power-law distributions are all exactly the stationary
solutions based on the two-variable Langevin equations. | cond-mat_stat-mech |
Critical Properties of the Models of Small Magnetic Particles of the
Antiferromagnet MnF2: The static critical behavior of the models of small magnetic particles of the
real two sublattice antiferromagnet MnF2 is investigated by the Monte Carlo
method taking into account the interaction of the second nearest neighbors.
Systems with open boundaries are considered to estimate the influence of the
sizes of particles on the pattern of their critical behavior. The behavior of
thermodynamic functions in the phase transition region is investigated. The
data on the maxima of the temperature dependences of heat capacity and magnetic
susceptibility are shown to be insufficient to unambiguously determine the
effective temperture of the phase transition in the models of small magnetic
particles. This requires an additional investigation of the spatial orientation
of the sublattice (sublattices) magnetization vector for the models under
study. | cond-mat_stat-mech |
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