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Aspects of Nosé and Nosé-Hoover Dynamics Elucidated: Some paradoxical aspects of the Nos\'e and Nos\'e-Hoover dynamics of 1984 and
Dettmann's dynamics of 1996 are elucidated. Phase-space descriptions of
thermostated harmonic oscillator dynamics can be simultaneously expanding,
incompressible, or contracting, as is described here by a variety of three- and
four-dimensional phase-space models. These findings illustrate some surprising
consequences when Liouville's continuity equation is applied to Hamiltonian
flows. | cond-mat_stat-mech |
Optimized effective potential method with exact exchange and static RPA
correlation: We present a new density-functional method of the self-consistent
electronic-structure calculation which does not exploit any local density
approximations (LDA). We use the exchange-correlation energy which consists of
the exact exchange and the correlation energies in the random-phase
approximation. The functional derivative of the correlation energy with respect
to the density is obtained within a static approximation. For transition
metals, it is shown that the correlation potential gives rise to a large
contribution which has the opposite sign to the exchange potential. Resulting
eigenvalue dispersions and the magnetic moments are very close to those of
LDA's and the experiments. | cond-mat_stat-mech |
On the phase transition in the sublattice TASEP with stochastic blockage: We revisit the defect-induced nonequilibrium phase transition from a largely
homogeneous free-flow phase to a phase-separated congested phase in the
sublattice totally asymmetric simple exclusion process (TASEP) with local
deterministic bulk dynamics and a stochastic defect that mimicks a random
blockage. Exact results are obtained for the compressibility and density
correlations for a stationary grandcanonical ensemble given by the matrix
product ansatz. At the critical density the static compressibility diverges
while in the phase separated state above the critical point the compressibility
vanishes due to strong non-local correlations. These correlations arise from a
long range effective interaction between particles that appears in the
stationary state despite the locality of the microscopic dynamics. | cond-mat_stat-mech |
Coevolution of agents and networks: Opinion spreading and community
disconnection: We study a stochastic model for the coevolution of a process of opinion
formation in a population of agents and the network which underlies their
interaction. Interaction links can break when agents fail to reach an opinion
agreement. The structure of the network and the distribution of opinions over
the population evolve towards a state where the population is divided into
disconnected communities whose agents share the same opinion. The statistical
properties of this final state vary considerably as the model parameters are
changed. Community sizes and their internal connectivity are the quantities
used to characterize such variations. | cond-mat_stat-mech |
Exact stochastic Liouville and Schrödinger equations for open
systems: An universal form of kinetic equation for open systems is considered which
naturally unifies classical and quantum cases and allows to extend concept of
wave function to open quantum systems. Corresponding stochastic Schr\"{o}dinger
equation is derived and illustrated by the example of inelastic scattering in
quantum conduction channel. | cond-mat_stat-mech |
Dynamical Heterogeneities Below the Glass Transition: We present molecular dynamics simulations of a binary Lennard-Jones mixture
at temperatures below the kinetic glass transition. The ``mobility'' of a
particle is characterized by the amplitude of its fluctuation around its
average position. The 5% particles with the largest/smallest mean amplitude are
thus defined as the relatively most mobile/immobile particles. We investigate
for these 5% particles their spatial distribution and find them to be
distributed very heterogeneously in that mobile as well as immobile particles
form clusters. The reason for this dynamic heterogeneity is traced back to the
fact that mobile/immobile particles are surrounded by fewer/more neighbors
which form an effectively wider/narrower cage. The dependence of our results on
the length of the simulation run indicates that individual particles have a
characteristic mobility time scale, which can be approximated via the
non-Gaussian parameter. | cond-mat_stat-mech |
Direct evaluation of large-deviation functions: We introduce a numerical procedure to evaluate directly the probabilities of
large deviations of physical quantities, such as current or density, that are
local in time. The large-deviation functions are given in terms of the typical
properties of a modified dynamics, and since they no longer involve rare
events, can be evaluated efficiently and over a wider ranges of values. We
illustrate the method with the current fluctuations of the Totally Asymmetric
Exclusion Process and with the work distribution of a driven Lorentz gas. | cond-mat_stat-mech |
Quasi-phases and pseudo-transitions in one-dimensional models with
nearest neighbor interactions: There are some particular one-dimensional models, such as the
Ising-Heisenberg spin models with a variety of chain structures, which exhibit
unexpected behaviors quite similar to the first and second order phase
transition, which could be confused naively with an authentic phase transition.
Through the analysis of the first derivative of free energy, such as entropy,
magnetization, and internal energy, a "sudden" jump that closely resembles a
first-order phase transition at finite temperature occurs. However, by
analyzing the second derivative of free energy, such as specific heat and
magnetic susceptibility at finite temperature, it behaves quite similarly to a
second-order phase transition exhibiting an astonishingly sharp and fine peak.
The correlation length also confirms the evidence of this pseudo-transition
temperature, where a sharp peak occurs at the pseudo-critical temperature. We
also present the necessary conditions for the emergence of these quasi-phases
and pseudo-transitions. | cond-mat_stat-mech |
Random Networks Growing Under a Diameter Constraint: We study the growth of random networks under a constraint that the diameter,
defined as the average shortest path length between all nodes, remains
approximately constant. We show that if the graph maintains the form of its
degree distribution then that distribution must be approximately scale-free
with an exponent between 2 and 3. The diameter constraint can be interpreted as
an environmental selection pressure that may help explain the scale-free nature
of graphs for which data is available at different times in their growth. Two
examples include graphs representing evolved biological pathways in cells and
the topology of the Internet backbone. Our assumptions and explanation are
found to be consistent with these data. | cond-mat_stat-mech |
Ising and anisotropic Heisenberg magnets with mobile defects: Motivated by experiments on (Sr,Ca,La)_14 Cu_24 O_41, a two-dimensional Ising
model with mobile defects and a two-dimensional anisotropic Heisenberg
antiferromagnet have been proposed and studied recently. We extend previous
investigations by analysing phase diagrams of both models in external fields
using mainly Monte Carlo techniques. In the Ising case, the phase transition is
due to the thermal instability of defect stripes, in the Heisenberg case
additional spin-flop structures play an essential role. | cond-mat_stat-mech |
Mapping out of equilibrium into equilibrium in one-dimensional transport
models: Systems with conserved currents driven by reservoirs at the boundaries offer
an opportunity for a general analytic study that is unparalleled in more
general out of equilibrium systems. The evolution of coarse-grained variables
is governed by stochastic {\em hydrodynamic} equations in the limit of small
noise.} As such it is amenable to a treatment formally equal to the
semiclassical limit of quantum mechanics, which reduces the problem of finding
the full distribution functions to the solution of a set of Hamiltonian
equations. It is in general not possible to solve such equations explicitly,
but for an interesting set of problems (driven Symmetric Exclusion Process and
Kipnis-Marchioro-Presutti model) it can be done by a sequence of remarkable
changes of variables. We show that at the bottom of this `miracle' is the
surprising fact that these models can be taken through a non-local
transformation into isolated systems satisfying detailed balance, with
probability distribution given by the Gibbs-Boltzmann measure. This procedure
can in fact also be used to obtain an elegant solution of the much simpler
problem of non-interacting particles diffusing in a one-dimensional potential,
again using a transformation that maps the driven problem into an undriven one. | cond-mat_stat-mech |
An Entropic Approach To Classical Density Functional Theory: The classical Density Functional Theory (DFT) is introduced as an application
of entropic inference for inhomogeneous fluids at thermal equilibrium. It is
shown that entropic inference reproduces the variational principle of DFT when
information about expected density of particles is imposed. This process
introduces an intermediate family of trial density-parametrized probability
distributions, and consequently an intermediate entropy, from which the
preferred one is found using the method of Maximum Entropy (MaxEnt). As an
application, the DFT model for slowly varying density is provided, and its
approximation scheme is discussed. | cond-mat_stat-mech |
Model study on steady heat capacity in driven stochastic systems: We explore two- and three-state Markov models driven out of thermal
equilibrium by non-potential forces to demonstrate basic properties of the
steady heat capacity based on the concept of quasistatic excess heat. It is
shown that large enough driving forces can make the steady heat capacity
negative. For both the low- and high-temperature regimes we propose an
approximative thermodynamic scheme in terms of "dynamically renormalized"
effective energy levels. | cond-mat_stat-mech |
Dispersive diffusion controlled distance dependent recombination in
amorphous semiconductors: The photoluminescence in amorphous semiconductors decays according to power
law $t^{-delta}$ at long times. The photoluminescence is controlled by
dispersive transport of electrons. The latter is usually characterized by the
power $alpha$ of the transient current observed in the time-of-flight
experiments. Geminate recombination occurs by radiative tunneling which has a
distance dependence. In this paper, we formulate ways to calculate reaction
rates and survival probabilities in the case carriers execute dispersive
diffusion with long-range reactivity. The method is applied to obtain tunneling
recombination rates under dispersive diffusion. The theoretical condition of
observing the relation $delta = alpha/2 + 1$ is obtained and theoretical
recombination rates are compared to the kinetics of observed photoluminescence
decay in the whole time range measured. | cond-mat_stat-mech |
Advantages and challenges in coupling an ideal gas to atomistic models
in adaptive resolution simulations: In adaptive resolution simulations, molecular fluids are modeled employing
different levels of resolution in different subregions of the system. When
traveling from one region to the other, particles change their resolution on
the fly. One of the main advantages of such approaches is the computational
efficiency gained in the coarse-grained region. In this respect the best
coarse-grained system to employ in the low resolution region would be the ideal
gas, making intermolecular force calculations in the coarse-grained subdomain
redundant. In this case, however, a smooth coupling is challenging due to the
high energetic imbalance between typical liquids and a system of
non-interacting particles. In the present work, we investigate this approach,
using as a test case the most biologically relevant fluid, water. We
demonstrate that a successful coupling of water to the ideal gas can be
achieved with current adaptive resolution methods, and discuss the issues that
remain to be addressed. | cond-mat_stat-mech |
Fractional Path Integral Monte Carlo: Fractional derivatives are nonlocal differential operators of real order that
often appear in models of anomalous diffusion and a variety of nonlocal
phenomena. Recently, a version of the Schr\"odinger Equation containing a
fractional Laplacian has been proposed. In this work, we develop a Fractional
Path Integral Monte Carlo algorithm that can be used to study the finite
temperature behavior of the time-independent Fractional Schr\"odinger Equation
for a variety of potentials. In so doing, we derive an analytic form for the
finite temperature fractional free particle density matrix and demonstrate how
it can be sampled to acquire new sets of particle positions. We employ this
algorithm to simulate both the free particle and $^{4}$He (Aziz) Hamiltonians.
We find that the fractional Laplacian strongly encourages particle
delocalization, even in the presence of interactions, suggesting that
fractional Hamiltonians may manifest atypical forms of condensation. Our work
opens the door to studying fractional Hamiltonians with arbitrarily complex
potentials that escape analytical solutions. | cond-mat_stat-mech |
Active Brownian Particles Escaping a Channel in Single File: Active particles may happen to be confined in channels so narrow that they
cannot overtake each other (Single File conditions). This interesting situation
reveals nontrivial physical features as a consequence of the strong
inter-particle correlations developed in collective rearrangements. We consider
a minimal model for active Brownian particles with the aim of studying the
modifications introduced by activity with respect to the classical (passive)
Single File picture. Depending on whether their motion is dominated by
translational or rotational diffusion, we find that active Brownian particles
in Single File may arrange into clusters which are continuously merging and
splitting ({\it active clusters}) or merely reproduce passive-motion paradigms,
respectively. We show that activity convey to self-propelled particles a
strategic advantage for trespassing narrow channels against external biases
(e.g., the gravitational field). | cond-mat_stat-mech |
Spontaneous symmetry breaking in the finite, lattice quantum sine-Gordon
model: The spontaneous breaking of a global discrete translational symmetry in the
finite, lattice quantum sine-Gordon model is demonstrated by a density matrix
renormalization group. A phase diagram in the coupling constant - inverse
system size plane is obtained. Comparison of the phase diagram with a
Woomany-Wyld finite-size scaling leads to an identification of the
Berezinskii-Kosterlitz-Thouless transition in the quantum sine-Gordon model as
the spontaneous symmetry breaking. | cond-mat_stat-mech |
Heat Conduction, and the Lack Thereof, in Time-Reversible Dynamical
Systems: Generalized Nosé-Hoover Oscillators with a Temperature Gradient: We use nonequilibrium molecular dynamics to analyze and illustrate the
qualitative differences between the one-thermostat and two-thermostat versions
of equilibrium and nonequilibrium (heat-conducting) harmonic oscillators.
Conservative nonconducting regions can coexist with dissipative heat conducting
regions in phase space with exactly the same imposed temperature field. | cond-mat_stat-mech |
Bose-Einstein Condensation in Classical Systems: It is shown, that Bose-Einstein statistical distributions can occur not only
in quantum system, but in classical systems as well. The coherent dynamics of
the system, or equivalently autocatalytic dynamics in momentum space of the
system is the main reason for the Bose-Einstein condensation. A coherence is
possible in both quantum and classical systems, and in both cases can lead to
Bose-Einstein statistical distribution. | cond-mat_stat-mech |
A Master Equation for Power Laws: We propose a new mechanism for generating power laws. Starting from a random
walk, we first outline a simple derivation of the Fokker-Planck equation. By
analogy, starting from a certain Markov chain, we derive a master equation for
power laws that describes how the number of cascades changes over time
(cascades are consecutive transitions that end when the initial state is
reached). The partial differential equation has a closed form solution which
gives an explicit dependence of the number of cascades on their size and on
time. Furthermore, the power law solution has a natural cut-off, a feature
often seen in empirical data. This is due to the finite size a cascade can have
in a finite time horizon. The derivation of the equation provides a
justification for an exponent equal to 2, which agrees well with several
empirical distributions, including Richardson's law on the size and frequency
of deadly conflicts. Nevertheless, the equation can be solved for any exponent
value. In addition, we propose an urn model where the number of consecutive
ball extractions follows a power law. In all cases, the power law is manifest
over the entire range of cascade sizes, as shown through log-log plots in the
frequency and rank distributions. | cond-mat_stat-mech |
Extended hydrodynamics from Enskog's equation: The bidimensional case: A heat conduction problem is studied using extended hydrodynamic equations
obtained from Enskog's equation for a simple case of two planar systems in
contact through a porous wall. One of the systems is in equilibrium and the
other one in a steady conductive state. The example is used to put to test the
predictions which has been made with a new thermodynamic formalism. | cond-mat_stat-mech |
Anomalous diffusion of scaled Brownian tracers: A model for anomalous transport of tracer particles diffusing in complex
media in two dimensions is proposed. The model takes into account the
characteristics of persistent motion that active bath transfer to the tracer,
thus the model proposed in here extends active Brownian motion, for which the
stochastic dynamics of the orientation of the propelling force is described by
scale Brownian motion (sBm), identified by a the time dependent diffusivity of
the form $D_\beta\propto t^{\beta-1}$, $\beta>0$. If $\beta\neq1$, sBm is
highly non-stationary and suitable to describe such a non-equilibrium dynamics
induced by complex media. In this paper we provide analytical calculations and
computer simulations to show that genuine anomalous diffusion emerge in the
long-time regime, with a time scaling of the mean square displacement
$t^{2-\beta}$, while ballistic transport $t^2$, characteristic of persistent
motion, is found in the short-time one. An analysis of the time dependence of
the kurtosis, and intermediate scattering function of the positions
distribution, as well as the propulsion auto-correlation function, which
defines the effective persistence time, are provided. | cond-mat_stat-mech |
Dynamics of two qubits in a spin-bath of Quantum anisotropic Heisenberg
XY coupling type: The dynamics of two 1/2-spin qubits under the influence of a quantum
Heisenberg XY type spin-bath is studied. After the Holstein-Primakoff
transformation, a novel numerical polynomial scheme is used to give the
time-evolution calculation of the center qubits initially prepared in a product
state or a Bell state. Then the concurrence of the two qubits, the
$z$-component moment of either of the subsystem spins and the fidelity of the
subsystem are shown, which exhibit sensitive dependence on the anisotropic
parameter, the temperature, the coupling strength and the initial state. It is
found that (i) the larger the anisotropic parameter $\gamma$, the bigger the
probability of maintaining the initial state of the two qubits; (ii) with
increasing temperature $T$, the bath plays a more strong destroy effect on the
dynamics of the subsystem, so does the interaction $g_0$ between the subsystem
and the bath; (iii) the time evolution of the subsystem is dependent on the
initial state. The revival of the concurrence does not always means the restore
of the state. Further, the dynamical properties of the subsystem should be
judged by the combination of concurrence and fidelity. | cond-mat_stat-mech |
Dynamic critical properties of a one-dimensional probabilistic cellular
automaton: Dynamic properties of a one-dimensional probabilistic cellular automaton are
studied by monte-carlo simulation near a critical point which marks a
second-order phase transition from a active state to a effectively unique
absorbing state. Values obtained for the dynamic critical exponents indicate
that the transition belongs to the universality class of directed percolation.
Finally the model is compared with a previously studied one to show that a
difference in the nature of the absorbing states places them in different
universality classes. | cond-mat_stat-mech |
Non-monotonic dependence on disorder in biased diffusion on small-world
networks: We report numerical simulations of a strongly biased diffusion process on a
one-dimensional substrate with directed shortcuts between randomly chosen
sites, i.e. with a small-world-like structure. We find that, unlike many other
dynamical phenomena on small-world networks, this process exhibits
non-monotonic dependence on the density of shortcuts. Specifically, the
diffusion time over a finite length is maximal at an intermediate density. This
density scales with the length in a nontrivial manner, approaching zero as the
length grows. Longer diffusion times for intermediate shortcut densities can be
ascribed to the formation of cyclic paths where the diffusion process becomes
occasionally trapped. | cond-mat_stat-mech |
Thermal Transport in a Noncommutative Hydrodynamics: We find the hydrodynamic equations of a system of particles constrained to be
in the lowest Landau level. We interpret the hydrodynamic theory as a
Hamiltonian system with the Poisson brackets between the hydrodynamic variables
determined from the noncommutativity of space. We argue that the most general
hydrodynamic theory can be obtained from this Hamiltonian system by allowing
the Righi-Leduc coefficient to be an arbitrary function of thermodynamic
variables. We compute the Righi-Leduc coefficients at high temperatures and
show that it satisfies the requirements of particle-hole symmetry, which we
outline. | cond-mat_stat-mech |
Sojourn probabilities in tubes and pathwise irreversibility for Itô
processes: The sojourn probability of an It\^o diffusion process, i.e. its probability
to remain in the tubular neighborhood of a smooth path, is a central quantity
in the study of path probabilities. For $N$-dimensional It\^o processes with
state-dependent full-rank diffusion tensor, we derive a general expression for
the sojourn probability in tubes whose radii are small but finite, and fixed by
the metric of the ambient Euclidean space. The central quantity in our study is
the exit rate at which trajectories leave the tube for the first time. This has
an interpretation as a Lagrangian and can be measured directly in experiment,
unlike previously defined sojourn probabilities which depend on prior knowledge
of the state-dependent diffusivity. We find that while in the limit of
vanishing tube radius the ratio of sojourn probabilities for a pair of distinct
paths is in general divergent, the same for a path and its time-reversal is
always convergent and finite. This provides a pathwise definition of
irreversibility for It\^o processes that is agnostic to the state-dependence of
the diffusivity. For one-dimensional systems we derive an explicit expression
for our Lagrangian in terms of the drift and diffusivity, and find that our
result differs from previously reported multiplicative-noise Lagrangians. We
confirm our result by comparing to numerical simulations, and relate our theory
to the Stratonovich Lagrangian for multiplicative noise. For one-dimensional
systems, we discuss under which conditions the vanishing-radius limiting ratio
of sojourn probabilities for a pair of forward and backward paths recovers the
established pathwise entropy production. Finally, we demonstrate for our
one-dimensional example system that the most probable tube for a barrier
crossing depends sensitively on the tube radius, and hence on the tolerated
amount of fluctuations around the smooth reference path. | cond-mat_stat-mech |
Critical aging of a ferromagnetic system from a completely ordered state: We adapt the non-linear $\sigma$ model to study the nonequilibrium critical
dynamics of O(n) symmetric ferromagnetic system. Using the renormalization
group analysis in $d=2+\epsilon$ dimensions we investigate the pure relaxation
of the system starting from a completely ordered state. We find that the
average magnetization obeys the long-time scaling behavior almost immediately
after the system starts to evolve while the correlation and response functions
demonstrate scaling behavior which is typical for aging phenomena. The
corresponding fluctuation-dissipation ratio is computed to first order in
$\epsilon$ and the relation between transverse and longitudinal fluctuations is
discussed. | cond-mat_stat-mech |
Collective effects in spin-crossover chains with exchange interaction: The collective properties of spin-crossover chains are studied.
Spin-crossover compounds contain ions with a low-spin ground state and low
lying high-spin excited states and are of interest for molecular memory
applications. Some of them naturally form one-dimensional chains. Elastic
interaction and Ising exchange interaction are taken into account. The
transfer-matrix approach is used to calculate the partition function, the
fraction of ions in the high-spin state, the magnetization, susceptibility,
etc., exactly. The high-spin-low-spin degree of freedom leads to collective
effects not present in simple spin chains. The ground-state phase diagram is
mapped out and compared to the case with Heisenberg exchange interaction. The
various phases give rise to characteristic behavior at nonzero temperatures,
including sharp crossovers between low- and high-temperature regimes. A
Curie-Weiss law for the susceptibility is derived and the paramagnetic Curie
temperature is calculated. Possible experiments to determine the exchange
coupling are discussed. | cond-mat_stat-mech |
Pattern description of the ground state properties of the
one-dimensional axial next-nearest-neighbor Ising model in a transverse field: The description and understanding of the consequences of competing
interactions in various systems, both classical and quantum, are notoriously
difficult due to insufficient information involved in conventional concepts,
for example, order parameters and/or correlation functions. Here we go beyond
these conventional language and present a pattern picture to describe and
understand the frustration physics by taking the one-dimensional (1D) axial
next-nearest-neighbor Ising (ANNNI) model in a transverse field as an example.
The system is dissected by the patterns, obtained by diagnonalizing the model
Hamiltonian in an operator space with a finite lattice size $4n$ ($n$: natural
number) and periodic boundary condition. With increasing the frustration
parameter, the system experiences successively various phases/metastates,
identified respectively as those with zero, two, four, $\cdots$, $2n$
domains/kinks, where the first is the ferromagnetic phase and the last the
antiphase. Except for the ferromagnetic phase and antiphase, the others should
be metastates, whose transitions are crossing over in nature. The results
clarify the controversial issues about the phases in the 1D ANNNI model and
provide a starting point to study more complicated situations, for example, the
frustration systems in high dimensions. | cond-mat_stat-mech |
Large deviations for a stochastic model of heat flow: We investigate a one dimensional chain of $2N$ harmonic oscillators in which
neighboring sites have their energies redistributed randomly. The sites $-N$
and $N$ are in contact with thermal reservoirs at different temperature
$\tau_-$ and $\tau_+$. Kipnis, Marchioro, and Presutti \cite{KMP} proved that
this model satisfies {}Fourier's law and that in the hydrodynamical scaling
limit, when $N \to \infty$, the stationary state has a linear energy density
profile $\bar \theta(u)$, $u \in [-1,1]$. We derive the large deviation
function $S(\theta(u))$ for the probability of finding, in the stationary
state, a profile $\theta(u)$ different from $\bar \theta(u)$. The function
$S(\theta)$ has striking similarities to, but also large differences from, the
corresponding one of the symmetric exclusion process. Like the latter it is
nonlocal and satisfies a variational equation. Unlike the latter it is not
convex and the Gaussian normal fluctuations are enhanced rather than suppressed
compared to the local equilibrium state. We also briefly discuss more general
model and find the features common in these two and other models whose
$S(\theta)$ is known. | cond-mat_stat-mech |
Density relaxation in conserved Manna sandpiles: We study relaxation of long-wavelength density perturbations in one
dimensional conserved Manna sandpile. Far from criticality where correlation
length $\xi$ is finite, relaxation of density profiles having wave numbers $k
\rightarrow 0$ is diffusive, with relaxation time $\tau_R \sim k^{-2}/D$ with
$D$ being the density-dependent bulk-diffusion coefficient. Near criticality
with $k \xi \gsim 1$, the bulk diffusivity diverges and the transport becomes
anomalous; accordingly, the relaxation time varies as $\tau_R \sim k^{-z}$,
with the dynamical exponent $z=2-(1-\beta)/\nu_{\perp} < 2$, where $\beta$ is
the critical order-parameter exponent and and $\nu_{\perp}$ is the critical
correlation-length exponent. Relaxation of initially localized density profiles
on infinite critical background exhibits a self-similar structure. In this
case, the asymptotic scaling form of the time-dependent density profile is
analytically calculated: we find that, at long times $t$, the width $\sigma$ of
the density perturbation grows anomalously, i.e., $\sigma \sim t^{w}$, with the
growth exponent $\omega=1/(1+\beta) > 1/2$. In all cases, theoretical
predictions are in reasonably good agreement with simulations. | cond-mat_stat-mech |
Effects of the non-Markovianity and non-Gaussianity of active
environmental noises on engine performance: An active environment is a reservoir containing \emph{active} materials, such
as bacteria and Janus particles. Given the self-propelled motion of these
materials, powered by chemical energy, an active environment has unique,
nonequilibrium environmental noise. Recently, studies on engines that harvest
energy from active environments have attracted a great deal of attention
because the theoretical and experimental findings indicate that these engines
outperform conventional ones. Studies have explored the features of active
environments essential for outperformance, such as the non-Gaussian or
non-Markovian nature of the active noise. However, these features have not yet
been systematically investigated in a general setting. Therefore, we
systematically study the effects of the non-Gaussianity and non-Markovianity of
active noise on engine performance. We show that non-Gaussianity is irrelevant
to the performance of an engine driven by {any linear force (including a
harmonic trap) regardless of time dependency}, whereas non-Markovianity is
relevant. However, for a system driven by a general nonlinear force, both
non-Gaussianity and non-Markovianity enhance engine performance. Also, the
memory effect of an active reservoir should be considered when fabricating a
cyclic engine. | cond-mat_stat-mech |
Global topological control for synchronized dynamics on networks: A general scheme is proposed and tested to control the symmetry breaking
instability of a homogeneous solution of a spatially extended multispecies
model, defined on a network. The inherent discreteness of the space makes it
possible to act on the topology of the inter-nodes contacts to achieve the
desired degree of stabilization, without altering the dynamical parameters of
the model. Both symmetric and asymmetric couplings are considered. In this
latter setting the web of contacts is assumed to be balanced, for the
homogeneous equilibrium to exist. The performance of the proposed method are
assessed, assuming the Complex Ginzburg-Landau equation as a reference model.
In this case, the implemented control allows one to stabilize the synchronous
limit cycle, hence time-dependent, uniform solution. A system of coupled real
Ginzburg-Landau equations is also investigated to obtain the topological
stabilization of a homogeneous and constant fixed point. | cond-mat_stat-mech |
The noise intensity of a Markov chain: Stochastic transitions between discrete microscopic states play an important
role in many physical and biological systems. Often, these transitions lead to
fluctuations on a macroscopic scale. A classic example from neuroscience is the
stochastic opening and closing of ion channels and the resulting fluctuations
in membrane current. When the microscopic transitions are fast, the macroscopic
fluctuations are nearly uncorrelated and can be fully characterized by their
mean and noise intensity. We show how, for an arbitrary Markov chain, the noise
intensity can be determined from an algebraic equation, based on the transition
rate matrix. We demonstrate the validity of the theory using an analytically
tractable two-state Markovian dichotomous noise, an eight-state model for a
Calcium channel subunit (De Young-Keizer model), and Markov models of the
voltage-gated Sodium and Potassium channels as they appear in a stochastic
version of the Hodgkin-Huxley model. | cond-mat_stat-mech |
Phase diagram and critical exponents of a dissipative Ising spin chain
in a transverse magnetic field: We consider a one-dimensional Ising model in a transverse magnetic field
coupled to a dissipative heat bath. The phase diagram and the critical
exponents are determined from extensive Monte Carlo simulations. It is shown
that the character of the quantum phase transition is radically altered from
the corresponding non-dissipative model and the double-well coupled to a
dissipative heat bath with linear friction. Spatial couplings and the
dissipative dynamics combine to form a new quantum criticality. | cond-mat_stat-mech |
Palette-colouring: a belief-propagation approach: We consider a variation of the prototype combinatorial-optimisation problem
known as graph-colouring. Our optimisation goal is to colour the vertices of a
graph with a fixed number of colours, in a way to maximise the number of
different colours present in the set of nearest neighbours of each given
vertex. This problem, which we pictorially call "palette-colouring", has been
recently addressed as a basic example of problem arising in the context of
distributed data storage. Even though it has not been proved to be NP complete,
random search algorithms find the problem hard to solve. Heuristics based on a
naive belief propagation algorithm are observed to work quite well in certain
conditions. In this paper, we build upon the mentioned result, working out the
correct belief propagation algorithm, which needs to take into account the
many-body nature of the constraints present in this problem. This method
improves the naive belief propagation approach, at the cost of increased
computational effort. We also investigate the emergence of a satisfiable to
unsatisfiable "phase transition" as a function of the vertex mean degree, for
different ensembles of sparse random graphs in the large size ("thermodynamic")
limit. | cond-mat_stat-mech |
Giant spin current rectification due to the interplay of negative
differential conductance and a non-uniform magnetic field: In XXZ chains, spin transport can be significantly suppressed when the
interactions in the chain and the bias of the dissipative driving are large
enough. This phenomenon of negative differential conductance is caused by the
formation of two oppositely polarized ferromagnetic domains at the edges of the
chain. Here we show that this many-body effect, combined with a non-uniform
magnetic field, can allow a high degree of control of the spin current. In
particular, by studying all the possible combinations of a dichotomous local
magnetic field, we found that a configuration in which the magnetic field
points up for half of the chain and down for the other half, can result in
giant spin-current rectification, for example up to $10^8$ for a system with
$8$ spins. Our results show clear indications that the rectification can
increase with the system size. | cond-mat_stat-mech |
Kramers-Wannier Duality of Statistical Mechanics Applied to the Boolean
Satisfiability Problem of Computer Science: We present a novel application of the Kramers-Wannier duality on one of the
most important problems of computer science, the Boolean satisfiability problem
(SAT). More specifically, we focus on sharp-SAT or equivalently #SAT - the
problem of counting the number of solutions to a Boolean satisfaction formula.
#SAT can be cast into a statistical-mechanical language, where it reduces to
calculating the partition function of an Ising spin Hamiltonian with multi-spin
interactions. We show that Kramers-Wannier duality can be generalized to apply
to such multi-connected spin networks. We present an exact dual partner to #SAT
and explicitly verify their equivalence with a few simple examples. It is shown
that the NP-completeness of the original problem maps on the complexity of the
dual problem of enumerating the number of non-negative solutions to a
Diophantine system of equations. We discuss the implications of this duality
and the prospects of similar dualities applied to computer science problems. | cond-mat_stat-mech |
Virial statistical description of non-extensive hierarchical systems: In a first part the scope of classical thermodynamics and statistical
mechanics is discussed in the broader context of formal dynamical systems,
including computer programmes. In this context classical thermodynamics appears
as a particular theory suited to a subset of all dynamical systems. A
statistical mechanics similar to the one derived with the microcanonical
ensemble emerges from dynamical systems provided it contains, 1) a finite
non-integrable part of its phase space which is, 2) ergodic at a satisfactory
degree after a finite time. The integrable part of phase space provides the
constraints that shape the particular system macroscopical properties, and the
chaotic part provides well behaved statistical properties over a relevant
finite time. More generic semi-ergodic systems lead to intermittent behaviour,
thus may be unsuited for a statistical description of steady states. Following
these lines of thought, in a second part non-extensive hierarchical systems
with statistical scale-invariance and power law interactions are explored. Only
the virial constraint, consistent with their microdynamics, is included. No
assumptions of classical thermodynamics are used, in particular extensivity and
local homogeneity. In the limit of a large hierarchical range new constraints
emerge in some conditions that depend on the interaction law range. In
particular for the gravitational case, a velocity-site scaling relation is
derived which is consistant with the ones empirically observed in the fractal
interstellar medium. | cond-mat_stat-mech |
Dynamics of structural models with a long-range interaction: glassy
versus non-glassy behavior: By making use of the Langevin dynamics and its generating functional (GF)
formulation the influence of the long-range nature of the interaction on the
tendency of the glass formation is systematically investigated. In doing so two
types of models is considered: (i) the non-disordered model with a pure
repulsive type of interaction and (ii) the model with a randomly distributed
strength of interaction (a quenched disordered model). The long-ranged
potential of interaction is scaled with a number of particles $N$ in such a way
as to enable for GF the saddle-point treatment as well as the systematic 1/N -
expansion around it. We show that the non-disordered model has no glass
transition which is in line with the mean-field limit of the mode - coupling
theory (MCT) predictions. On the other hand the model with a long-range
interaction which above that has a quenched disorder leads to MC - equations
which are generic for the $p$ - spin glass model and polymeric manifold in a
random media. | cond-mat_stat-mech |
The influence of measurement error on Maxwell's demon: In any general cycle of measurement, feedback and erasure, the measurement
will reduce the entropy of the system when information about the state is
obtained, while erasure, according to Landauer's principle, is accompanied by a
corresponding increase in entropy due to the compression of logical and
physical phase space. The total process can in principle be fully reversible. A
measurement error reduces the information obtained and the entropy decrease in
the system. The erasure still gives the same increase in entropy and the total
process is irreversible. Another consequence of measurement error is that a bad
feedback is applied, which further increases the entropy production if the
proper protocol adapted to the expected error rate is not applied. We consider
the effect of measurement error on a realistic single-electron box Szilard
engine. We find the optimal protocol for the cycle as a function of the desired
power $P$ and error $\epsilon$, as well as the existence of a maximal power
$P^{\max}$. | cond-mat_stat-mech |
A large deviation perspective on ratio observables in reset processes:
robustness of rate functions: We study large deviations of a ratio observable in discrete-time reset
processes. The ratio takes the form of a current divided by the number of reset
steps and as such it is not extensive in time. A large deviation rate function
can be derived for this observable via contraction from the joint probability
density function of current and number of reset steps. The ratio rate function
is differentiable and we argue that its qualitative shape is 'robust', i.e. it
is generic for reset processes regardless of whether they have short- or
long-range correlations. We discuss similarities and differences with the rate
function of the efficiency in stochastic thermodynamics. | cond-mat_stat-mech |
Critical branching processes in digital memcomputing machines: Memcomputing is a novel computing paradigm that employs time non-locality
(memory) to solve combinatorial optimization problems. It can be realized in
practice by means of non-linear dynamical systems whose point attractors
represent the solutions of the original problem. It has been previously shown
that during the solution search digital memcomputing machines go through a
transient phase of avalanches (instantons) that promote dynamical long-range
order. By employing mean-field arguments we predict that the distribution of
the avalanche sizes follows a Borel distribution typical of critical branching
processes with exponent $\tau= 3/2$. We corroborate this analysis by solving
various random 3-SAT instances of the Boolean satisfiability problem. The
numerical results indicate a power-law distribution with exponent $\tau = 1.51
\pm 0.02$, in very good agreement with the mean-field analysis. This indicates
that memcomputing machines self-tune to a critical state in which avalanches
are characterized by a branching process, and that this state persists across
the majority of their evolution. | 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 |
Euclidean operator growth and quantum chaos: We consider growth of local operators under Euclidean time evolution in
lattice systems with local interactions. We derive rigorous bounds on the
operator norm growth and then proceed to establish an analog of the
Lieb-Robinson bound for the spatial growth. In contrast to the Minkowski case
when ballistic spreading of operators is universal, in the Euclidean case
spatial growth is system-dependent and indicates if the system is integrable or
chaotic. In the integrable case, the Euclidean spatial growth is at most
polynomial. In the chaotic case, it is the fastest possible: exponential in 1D,
while in higher dimensions and on Bethe lattices local operators can reach
spatial infinity in finite Euclidean time. We use bounds on the Euclidean
growth to establish constraints on individual matrix elements and operator
power spectrum. We show that one-dimensional systems are special with the power
spectrum always being superexponentially suppressed at large frequencies.
Finally, we relate the bound on the Euclidean growth to the bound on the growth
of Lanczos coefficients. To that end, we develop a path integral formalism for
the weighted Dyck paths and evaluate it using saddle point approximation. Using
a conjectural connection between the growth of the Lanczos coefficients and the
Lyapunov exponent controlling the growth of OTOCs, we propose an improved bound
on chaos valid at all temperatures. | cond-mat_stat-mech |
Exit versus escape in a stochastic dynamical system of neuronal networks
explains heterogenous bursting intervals: Neuronal networks can generate burst events. It remains unclear how to
analyse interburst periods and their statistics. We study here the phase-space
of a mean-field model, based on synaptic short-term changes, that exhibit burst
and interburst dynamics and we identify that interburst corresponds to the
escape from a basin of attraction. Using stochastic simulations, we report here
that the distribution of the these durations do not match with the time to
reach the boundary. We further analyse this phenomenon by studying a generic
class of two-dimensional dynamical systems perturbed by small noise that
exhibits two peculiar behaviors: 1- the maximum associated to the probability
density function is not located at the point attractor, which came as a
surprise. The distance between the maximum and the attractor increases with the
noise amplitude $\sigma$, as we show using WKB approximation and numerical
simulations. 2- For such systems, exiting from the basin of attraction is not
sufficient to characterize the entire escape time, due to trajectories that can
return several times inside the basin of attraction after crossing the
boundary, before eventually escaping far away. To conclude, long-interburst
durations are inherent properties of the dynamics and sould be expected in
empirical time series. | cond-mat_stat-mech |
Charged complexes at the surface of liquid helium: Charged clusters in liquid helium in an external electric field form a
two-dimensional system below the helium surface. This 2D system undergoes a
phase transition from a liquid to a Wigner crystal at rather high temperatures.
Contrary to the electron Wigner crystal, the Wigner lattice of charged clusters
can be detected directly. | cond-mat_stat-mech |
Does a Single Eigenstate of a Hamiltonian Encode the Critical Behaviour
of its Finite-Temperature Phase Transition?: Recent work on the subject of isolated quantum thermalization has suggested
that an individual energy eigenstate of a non-integrable quantum system may
encode a significant amount of information about that system's Hamiltonian. We
provide a theoretical argument, along with supporting numerics, that this
information includes the critical behaviour of a system with a second-order,
finite-temperature phase transition. | cond-mat_stat-mech |
Conditional maximum-entropy method for selecting prior distributions in
Bayesian statistics: The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is
formulated for selecting prior probability distributions in Bayesian statistics
for parameter estimation. This method is inspired by a statistical-mechanical
approach to systems governed by dynamics with largely-separated time scales and
is based on three key concepts: conjugate pairs of variables, dimensionless
integration measures with coarse-graining factors and partial maximization of
the joint entropy. The method enables one to calculate a prior purely from a
likelihood in a simple way. It is shown in particular how it not only yields
Jeffreys's rules but also reveals new structures hidden behind them. | cond-mat_stat-mech |
Energy partition for anharmonic, undamped, classical oscillators: Using stochastic methods, general formulas for average kinetic and potential
energies for anharmonic, undamped (frictionless), classical oscillators are
derived. It is demonstrated that for potentials of $|x|^\nu$ ($\nu>0$) type
energies are equipartitioned for the harmonic potential only. For potential
wells weaker than parabolic potential energy dominates, while for potentials
stronger than parabolic kinetic energy prevails. Due to energy conservation,
the variances of kinetic and potential energies are equal. In the limiting case
of the infinite rectangular potential well ($\nu\to\infty$) the whole energy is
stored in the form of the kinetic energy and variances of energy distributions
vanish. | cond-mat_stat-mech |
On the coexistence of dipolar frustration and criticality in
ferromagnets: In real magnets the tendency towards ferromagnetism, promoted by exchange
coupling, is usually frustrated by dipolar interaction. As a result, the
uniformly ordered phase is replaced by modulated (multi-domain) phases,
characterized by different order parameters rather than the global
magnetization. The transitions occurring within those modulated phases and
towards the disordered phase are generally not of second-order type.
Nevertheless, strong experimental evidence indicates that a standard critical
behavior is recovered when comparatively small fields are applied that
stabilize the uniform phase. The resulting power laws are observed with respect
to a putative critical point that falls in the portion of the phase diagram
occupied by modulated phases, in line with an avoided-criticality scenario.
Here we propose a generalization of the scaling hypothesis for ferromagnets,
which explains this observation assuming that the dipolar interaction acts as a
relevant field, in the sense of renormalization group. | cond-mat_stat-mech |
Particle escapes in an open quantum network via multiple leads: Quantum escapes of a particle from an end of a one-dimensional finite region
to $N$ number of semi-infinite leads are discussed by a scattering theoretical
approach. Depending on a potential barrier amplitude at the junction, the
probability $P(t)$ for a particle to remain in the finite region at time $t$
shows two different decay behaviors after a long time; one is proportional to
$N^{2}/t^{3}$ and another is proportional to $1/(N^{2}t)$. In addition, the
velocity $V(t)$ for a particle to leave from the finite region, defined from a
probability current of the particle position, decays in power $\sim 1/t$
asymptotically in time, independently of the number $N$ of leads and the
initial wave function, etc. For a finite time, the probability $P(t)$ decays
exponentially in time with a smaller decay rate for more number $N$ of leads,
and the velocity $V(t)$ shows a time-oscillation whose amplitude is larger for
more number $N$ of leads. Particle escapes from the both ends of a finite
region to multiple leads are also discussed by using a different boundary
condition. | cond-mat_stat-mech |
Universal entanglement signatures of interface conformal field theories: An interface connecting two distinct conformal field theories hosts rich
critical behaviors. In this work, we investigate the entanglement properties of
such critical interface theories for probing the underlying universality. As
inspired by holographic perspectives, we demonstrate vital features of various
entanglement measures regarding such interfaces based on several paradigmatic
lattice models. Crucially, for two subsystems adjacent at the interface, the
mutual information and the reflected entropy exhibit identical leading
logarithmic scaling, giving an effective interface central charge that takes
the same value as the smaller central charge of the two conformal field
theories. Our work demonstrates that the entanglement measure offers a powerful
tool to explore the rich physics in critical interface theories. | cond-mat_stat-mech |
Exit versus escape in a stochastic dynamical system of neuronal networks
explains heterogenous bursting intervals: Neuronal networks can generate burst events. It remains unclear how to
analyse interburst periods and their statistics. We study here the phase-space
of a mean-field model, based on synaptic short-term changes, that exhibit burst
and interburst dynamics and we identify that interburst corresponds to the
escape from a basin of attraction. Using stochastic simulations, we report here
that the distribution of the these durations do not match with the time to
reach the boundary. We further analyse this phenomenon by studying a generic
class of two-dimensional dynamical systems perturbed by small noise that
exhibits two peculiar behaviors: 1- the maximum associated to the probability
density function is not located at the point attractor, which came as a
surprise. The distance between the maximum and the attractor increases with the
noise amplitude $\sigma$, as we show using WKB approximation and numerical
simulations. 2- For such systems, exiting from the basin of attraction is not
sufficient to characterize the entire escape time, due to trajectories that can
return several times inside the basin of attraction after crossing the
boundary, before eventually escaping far away. To conclude, long-interburst
durations are inherent properties of the dynamics and sould be expected in
empirical time series. | cond-mat_stat-mech |
Weighted-ensemble Brownian dynamics simulation: Sampling of rare events
in non-equilibrium systems: We provide an algorithm based on weighted-ensemble (WE) methods, to
accurately sample systems at steady state. Applying our method to different
one- and two-dimensional models, we succeed to calculate steady state
probabilities of order $10^{-300}$ and reproduce Arrhenius law for rates of
order $10^{-280}$. Special attention is payed to the simulation of
non-potential systems where no detailed balance assumption exists. For this
large class of stochastic systems, the stationary probability distribution
density is often unknown and cannot be used as preknowledge during the
simulation. We compare the algorithms efficiency with standard Brownian
dynamics simulations and other WE methods. | cond-mat_stat-mech |
Boundary polarization in the six-vertex model: Vertical-arrow fluctuations near the boundaries in the six-vertex model on
the two-dimensional $N \times N$ square lattice with the domain wall boundary
conditions are considered. The one-point correlation function (`boundary
polarization') is expressed via the partition function of the model on a
sublattice. The partition function is represented in terms of standard objects
in the theory of orthogonal polynomials. This representation is used to study
the large N limit: the presence of the boundary affects the macroscopic
quantities of the model even in this limit. The logarithmic terms obtained are
compared with predictions from conformal field theory. | cond-mat_stat-mech |
Random sequential adsorption of straight rigid rods on a simple cubic
lattice: Random sequential adsorption of straight rigid rods of length $k$ ($k$-mers)
on a simple cubic lattice has been studied by numerical simulations and
finite-size scaling analysis. The calculations were performed by using a new
theoretical scheme, whose accuracy was verified by comparison with rigorous
analytical data. The results, obtained for \textit{k} ranging from 2 to 64,
revealed that (i) in the case of dimers ($k=2$), the jamming coverage is
$\theta_j=0.918388(16)$. Our estimate of $\theta_j$ differs significantly from
the previously reported value of $\theta_j=0.799(2)$ [Y. Y. Tarasevich and V.
A. Cherkasova, Eur. Phys. J. B \textbf{60}, 97 (2007)]; (ii) $\theta_j$
exhibits a decreasing function when it is plotted in terms of the $k$-mer size,
being $\theta_j (\infty)= 0.4045(19)$ the value of the limit coverage for large
$k$'s; and (iii) the ratio between percolation threshold and jamming coverage
shows a non-universal behavior, monotonically decreasing with increasing $k$. | cond-mat_stat-mech |
Thermal Casimir interactions for higher derivative field Lagrangians:
generalized Brazovskii models: We examine the Casimir effect for free statistical field theories which have
Hamiltonians with second order derivative terms. Examples of such Hamiltonians
arise from models of non-local electrostatics, membranes with non-zero bending
rigidities and field theories of the Brazovskii type that arise for polymer
systems. The presence of a second derivative term means that new types of
boundary conditions can be imposed, leading to a richer phenomenology of
interaction phenomena. In addition zero modes can be generated that are not
present in standard first derivative models, and it is these zero modes which
give rise to long range Casimir forces. Two physically distinct cases are
considered: (i) unconfined fields, usually considered for finite size embedded
inclusions in an infinite fluctuating medium, here in a two plate geometry the
fluctuating field exists both inside and outside the plates, (ii) confined
fields, where the field is absent outside the slab confined between the two
plates. We show how these two physically distinct cases are mathematically
related and discuss a wide range of commonly applied boundary conditions. We
concentrate our analysis to the critical region where the underlying bulk
Hamiltonian has zero modes and show that very exotic Casimir forces can arise,
characterised by very long range effects and oscillatory behavior that can lead
to strong metastability in the system. | cond-mat_stat-mech |
Contact process on generalized Fibonacci chains: infinite-modulation
criticality and double-log periodic oscillations: We study the nonequilibrium phase transition of the contact process with
aperiodic transition rates using a real-space renormalization group as well as
Monte-Carlo simulations. The transition rates are modulated according to the
generalized Fibonacci sequences defined by the inflation rules A $\to$ AB$^k$
and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and
the nonequilibrium transition is in the clean directed percolation universality
class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a
complete theory of the resulting unconventional "infinite-modulation" critical
point which is characterized by activated dynamical scaling. Moreover,
observables such as the survival probability and the size of the active cloud
display pronounced double-log periodic oscillations in time which reflect the
discrete scale invariance of the aperiodic chains. We illustrate our theory by
extensive numerical results, and we discuss relations to phase transitions in
other quasiperiodic systems. | cond-mat_stat-mech |
Universal scaling in active single-file dynamics: We study the single-file dynamics of three classes of active particles:
run-and-tumble particles, active Brownian particles and active
Ornstein-Uhlenbeck particles. At high activity values, the particles,
interacting via purely repulsive and short-ranged forces, aggregate into
several motile and dynamical clusters of comparable size, and do not display
bulk phase-segregation. In this dynamical steady-state, we find that the
cluster size distribution of these aggregates is a scaled function of the
density and activity parameters across the three models of active particles
with the same scaling function. The velocity distribution of these motile
clusters is non-Gaussian. We show that the effective dynamics of these clusters
can explain the observed emergent scaling of the mean-squared displacement of
tagged particles for all the three models with identical scaling exponents and
functions. Concomitant with the clustering seen at high activities, we observe
that the static density correlation function displays rich structures,
including multiple peaks that are reminiscent of particle clustering induced by
effective attractive interactions, while the dynamical variant shows
non-diffusive scaling. Our study reveals a universal scaling behavior in the
single-file dynamics of interacting active particles. | cond-mat_stat-mech |
Full decoherence induced by local fields in open spin chains with strong
boundary couplings: We investigate an open $XYZ$ spin $1/2$ chain driven out of equilibrium by
boundary reservoirs targeting different spin orientations, aligned along the
principal axes of anisotropy. We show that by tuning local magnetic fields,
applied to spins at sites near the boundaries, one can change any
nonequilibrium steady state to a fully uncorrelated Gibbsian state at infinite
temperature. This phenomenon occurs for strong boundary coupling and on a
critical manifold in the space of the fields amplitudes. The structure of this
manifold depends on the anisotropy degree of the model and on the parity of the
chain size. | cond-mat_stat-mech |
Extension of the Lieb-Schultz-Mattis theorem: Lieb, Schultz and Mattis (LSM) studied the S=1/2 XXZ spin chain. Theorems of
LSM's paper can be applied to broader models. In the original LSM theorem it
was assumed the nonfrustrating system. However, reconsidering the LSM theorem,
we can extend the LSM theorem for frustrating systems.
Next, several researchers have tried to extend the LSM theorem for excited
states. In the cases $S^{z}_{T} = \pm 1,\pm 2 \cdots$, the lowest energy
eigenvalues are continuous for wave number $q$. But we find that their proofs
are insufficient, and we improve them.
In addition, we can prove the LSM theory without the assumption of the
discrete symmetry, which means that the LSM type theorems are applicable for
Dzyaloshinskii-Moriya type interactions or other nonsymmetric models. | cond-mat_stat-mech |
Staggered long-range order for diluted quantum spin models: We study an annealed site diluted quantum XY model with spin $S\in
\frac{1}{2}\mathbb{N}$. We find regions of the parameter space where, in spite
of being a priori favourable for a densely occupied state, phases with
staggered occupancy occur at low temperatures. | cond-mat_stat-mech |
Diffusion of two molecular species in a crowded environment: theory and
experiments: Diffusion of a two component fluid is studied in the framework of
differential equations, but where these equations are systematically derived
from a well-defined microscopic model. The model has a finite carrying capacity
imposed upon it at the mesoscopic level and this is shown to lead to non-linear
cross diffusion terms that modify the conventional Fickean picture. After
reviewing the derivation of the model, the experiments carried out to test the
model are described. It is found that it can adequately explain the dynamics of
two dense ink drops simultaneously evolving in a container filled with water.
The experiment shows that molecular crowding results in the formation of a
dynamical barrier that prevents the mixing of the drops. This phenomenon is
successfully captured by the model. This suggests that the proposed model can
be justifiably viewed as a generalization of standard diffusion to a
multispecies setting, where crowding and steric interferences are taken into
account. | cond-mat_stat-mech |
Drag forces in classical fields: Inclusions, or defects, moving at constant velocity through free classical
fields are shown to be subject to a drag force which depends on the field
dynamics and the coupling of the inclusion to the field. The results are used
to predict the drag exerted on inclusions, such as proteins, in lipid membranes
due to their interaction with height and composition fluctuations. The force,
measured in Monte Carlo simulations, on a point like magnetic field moving
through an Ising ferromagnet is also well explained by these results. | cond-mat_stat-mech |
Nonexistence of the non-Gaussian fixed point predicted by the RG field
theory in 4-epsilon dimensions: The Ginzburg-Landau phase transition model is considered in d=4-epsilon
dimensions within the renormalization group (RG) approach. The problem of
existence of the non-Gaussian fixed point is discussed. An equation is derived
from the first principles of the RG theory (under the assumption that the fixed
point exists) for calculation of the correction-to-scaling term in the
asymptotic expansion of the two-point correlation (Green's) function. It is
demonstrated clearly that, within the framework of the standard methods (well
justified in the vicinity of the fixed point) used in the perturbative RG
theory, this equation leads to an unremovable contradiction with the known RG
results. Thus, in its very basics, the RG field theory in 4-epsilon dimensions
is contradictory. To avoid the contradiction, we conclude that such a
non-Gaussian fixed point, as predicted by the RG field theory, does not exist.
Our consideration does not exclude existence of a different fixed point. | cond-mat_stat-mech |
Interface growth in two dimensions: A Loewner-equation approach: The problem of Laplacian growth in two dimensions is considered within the
Loewner-equation framework. Initially the problem of fingered growth recently
discussed by Gubiec and Szymczak [T. Gubiec and P. Szymczak, Phys. Rev. E 77,
041602 (2008)] is revisited and a new exact solution for a three-finger
configuration is reported. Then a general class of growth models for an
interface growing in the upper-half plane is introduced and the corresponding
Loewner equation for the problem is derived. Several examples are given
including interfaces with one or more tips as well as multiple growing
interfaces. A generalization of our interface growth model in terms of
``Loewner domains,'' where the growth rule is specified by a time evolving
measure, is briefly discussed. | cond-mat_stat-mech |
Bogolyubov approximation for diagonal model of an interacting Bose gas: We study, using the Bogolyubov approximation, the thermodynamic behaviour of
a superstable Bose system whose energy operator in the second-quantized form
contains a nonlinear expression in the occupation numbers operators. We prove
that for all values of the chemical potential satisfying $\mu > \lambda(0)$,
where $\lambda (0)\leq 0$ is the lowest energy value, the system undergoes
Bose--Einstein condensation. | cond-mat_stat-mech |
Phase Transitions in the Multicomponent Widom-Rowlinson Model and in
Hard Cubes on the BCC--Lattice: We use Monte Carlo techniques and analytical methods to study the phase
diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are
M species all with the same fugacity z and a nearest neighbor hard core
exclusion between unlike particles. Simulations show that for M greater or
equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M)
while for z > z_d(M) there are M demixed phases each consisting mostly of one
species. For M=2 there is a direct second order transition from the gas phase
to the demixed phase while for M greater or equal 3 the transition at z_d(M)
appears to be first order putting it in the Potts model universality class. For
M large, Pirogov-Sinai theory gives z_d(M) ~ M-2+2/(3M^2) + ... . In the
crystal phase the particles preferentially occupy one of the sublattices,
independent of species, i.e. spatial symmetry but not particle symmetry is
broken. For M to infinity this transition approaches that of the one component
hard cube gas with fugacity y = zM. We find by direct simulations of such a
system a transition at y_c ~ 0.71 which is consistent with the simulation
z_c(M) for large M. This transition appears to be always of the Ising type. | cond-mat_stat-mech |
Mass distribution exponents for growing trees: We investigate the statistics of trees grown from some initial tree by
attaching links to preexisting vertices, with attachment probabilities
depending only on the valence of these vertices. We consider the asymptotic
mass distribution that measures the repartition of the mass of large trees
between their different subtrees. This distribution is shown to be a broad
distribution and we derive explicit expressions for scaling exponents that
characterize its behavior when one subtree is much smaller than the others. We
show in particular the existence of various regimes with different values of
these mass distribution exponents. Our results are corroborated by a number of
exact solutions for particular solvable cases, as well as by numerical
simulations. | cond-mat_stat-mech |
Monte Carlo Chord Length Sampling for $d$-dimensional Markov binary
mixtures: The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method
that models the effects of stochastic media on particle transport by generating
on-the-fly the material interfaces seen by the random walkers during their
trajectories. This annealed disorder approach, which formally consists of
solving the approximate Levermore-Pomraning equations for linear particle
transport, enables a considerable speed-up with respect to transport in
quenched disorder, where ensemble-averaging of the Boltzmann equation with
respect to all possible realizations is needed. However, CLS intrinsically
neglects the correlations induced by the spatial disorder, so that the accuracy
of the solutions obtained by using this algorithm must be carefully verified
with respect to reference solutions based on quenched disorder realizations.
When the disorder is described by Markov mixing statistics, such comparisons
have been attempted so far only for one-dimensional geometries, of the rod or
slab type. In this work we extend these results to Markov media in
two-dimensional (extruded) and three-dimensional geometries, by revisiting the
classical set of benchmark configurations originally proposed by Adams, Larsen
and Pomraning, and extended by Brantley. In particular, we examine the
discrepancies between CLS and reference solutions for scalar particle flux and
transmission/reflection coefficients as a function of the material properties
of the benchmark specifications and of the system dimensionality. | cond-mat_stat-mech |
Single-ion anisotropy in Haldane chains and form factor of the O(3)
nonlinear sigma model: We consider spin-1 Haldane chains with single-ion anisotropy, which exists in
known Haldane chain materials. We develop a perturbation theory in terms of
anisotropy, where magnon-magnon interaction is important even in the low
temperature limit. The exact two-particle form factor in the O(3) nonlinear
sigma model leads to quantitative predictions on several dynamical properties
including dynamical structure factor and electron spin resonance frequency
shift. These agree very well with numerical results, and with experimental data
on the Haldane chain material Ni(C$_5$H$_{14}$N$_2$)$_2$N$_3$(PF$_6$). | cond-mat_stat-mech |
Singularities of the renormalization group flow for random elastic
manifolds: We consider the singularities of the zero temperature renormalization group
flow for random elastic manifolds. When starting from small scales, this flow
goes through two particular points $l^{*}$ and $l_{c}$, where the average value
of the random squared potential $<U^{2}>$ turnes negative ($l^{*}$) and where
the fourth derivative of the potential correlator becomes infinite at the
origin ($l_{c}$). The latter point sets the scale where simple perturbation
theory breaks down as a consequence of the competition between many metastable
states. We show that under physically well defined circumstances $l_{c}<l^{*}$
and thus the apparent renormalization of $<U^{2}>$ to negative values does not
take place. | cond-mat_stat-mech |
Deterministic particle flows for constraining stochastic nonlinear
systems: Devising optimal interventions for constraining stochastic systems is a
challenging endeavour that has to confront the interplay between randomness and
nonlinearity. Existing methods for identifying the necessary dynamical
adjustments resort either to space discretising solutions of ensuing partial
differential equations, or to iterative stochastic path sampling schemes. Yet,
both approaches become computationally demanding for increasing system
dimension. Here, we propose a generally applicable and practically feasible
non-iterative methodology for obtaining optimal dynamical interventions for
diffusive nonlinear systems. We estimate the necessary controls from an
interacting particle approximation to the logarithmic gradient of two forward
probability flows evolved following deterministic particle dynamics. Applied to
several biologically inspired models, we show that our method provides the
necessary optimal controls in settings with terminal-, transient-, or
generalised collective-state constraints and arbitrary system dynamics. | cond-mat_stat-mech |
Dimensional crossover in dipolar magnetic layers: We investigate the static critical behaviour of a uniaxial magnetic layer,
with finite thickness L in one direction, yet infinitely extended in the
remaining d dimensions. The magnetic dipole-dipole interaction is taken into
account. We apply a variant of Wilson's momentum shell renormalisation group
approach to describe the crossover between the critical behaviour of the 3-D
Ising, 2-d Ising, 3-D uniaxial dipolar, and the 2-d uniaxial dipolar
universality classes. The corresponding renormalisation group fixed points are
in addition to different effective dimensionalities characterised by distinct
analytic structures of the propagator, and are consequently associated with
varying upper critical dimensions. While the limiting cases can be discussed by
means of dimensional epsilon expansions with respect to the appropriate upper
critical dimensions, respectively, the crossover features must be addressed in
terms of the renormalisation group flow trajectories at fixed dimensionality d. | cond-mat_stat-mech |
On the apparent failure of the topological theory of phase transitions: The topological theory of phase transitions has its strong point in two
theorems proving that, for a wide class of physical systems, phase transitions
necessarily stem from topological changes of some submanifolds of configuration
space. It has been recently argued that the $2D$ lattice $\phi^4$-model
provides a counterexample that falsifies this theory. It is here shown that
this is not the case: the phase transition of this model stems from an
asymptotic ($N\to\infty$) change of topology of the energy level sets, in spite
of the absence of critical points of the potential in correspondence of the
transition energy. | cond-mat_stat-mech |
Tracer dispersion in two-dimensional rough fractures: Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures
with self-affine roughness is studied by analytic and numerical methods.
Numerical simulations were performed via the lattice-Boltzmann approach, using
a new boundary condition for tracer particles that improves the accuracy of the
method. The reduction in the diffusive transport, due to the fractal geometry
of the fracture surfaces, is analyzed for different fracture apertures. In the
limit of small aperture fluctuations we derive the correction to the diffusive
coefficient in terms of the tortuosity, which accounts for the irregular
geometry of the fractures. Dispersion is studied when the two fracture surfaces
are simple displaced normally to the mean fracture plane, and when there is a
lateral shift as well. Numerical results are analyzed using the
$\Lambda$-parameter, related to convective transport within the fracture, and
simple arguments based on lubrication approximation. At very low P\'eclet
number, in the case where fracture surfaces are laterally shifted, we show
using several different methods that convective transport reduces dispersion. | cond-mat_stat-mech |
On Conservation Laws, Relaxation and Pre-relaxation after a Quantum
Quench: We consider the time evolution following a quantum quench in spin-1/2 chains.
It is well known that local conservation laws constrain the dynamics and,
eventually, the stationary behavior of local observables. We show that some
widely studied models, like the quantum XY model, possess extra families of
local conservation laws in addition to the translation invariant ones. As a
consequence, the additional charges must be included in the generalized Gibbs
ensemble that describes the stationary properties. The effects go well beyond a
simple redefinition of the stationary state. The time evolution of a
non-translation invariant state under a (translation invariant) Hamiltonian
with a perturbation that weakly breaks the hidden symmetries underlying the
extra conservation laws exhibits pre-relaxation. In addition, in the limit of
small perturbation, the time evolution following pre-relaxation can be
described by means of a time-dependent generalized Gibbs ensemble. | cond-mat_stat-mech |
Metastable and Unstable Dynamics in multi-phase lattice Boltzmann: We quantitatively characterize the metastability in a multi-phase lattice
Boltzmann model. The structure factor of density fluctuations is theoretically
obtained and numerically verified to a high precision, for all simulated
wave-vectors and reduced temperatures. The static structure factor is found to
consistently diverge as the temperature approaches the critical-point or the
density approaches the spinodal line at a sub-critical temperature.
Theoretically predicted critical exponents are observed in both cases. Finally,
the phase separation in the unstable branch follows the same pattern, i.e. the
generation of interfaces with different topology, as observed in molecular
dynamics simulations. All results can be independently reproduced through the
``idea.deploy" framework https://github.com/lullimat/idea.deploy | cond-mat_stat-mech |
Counting edge modes via dynamics of boundary spin impurities: We study dynamics of the one-dimensional Ising model in the presence of
static symmetry-breaking boundary field via the two-time autocorrelation
function of the boundary spin. We find that the correlations decay as a power
law. We uncover a dynamical phase diagram where, upon tuning the strength of
the boundary field, we observe distinct power laws that directly correspond to
changes in the number of edge modes as the boundary and bulk magnetic field are
varied. We suggest how the universal physics can be demonstrated in current
experimental setups, such as Rydberg chains. | cond-mat_stat-mech |
Non-sinusoidal current and current reversals in a gating ratchet: In this work, the ratchet dynamics of Brownian particles driven by an
external sinusoidal (harmonic) force is investigated. The gating ratchet effect
is observed when another harmonic is used to modulate the spatially symmetric
potential in which the particles move. For small amplitudes of the harmonics,
it is shown that the current (average velocity) of particles exhibits a
sinusoidal shape as a function of a precise combination of the phases of both
harmonics. By increasing the amplitudes of the harmonics beyond the small-limit
regime, departures from the sinusoidal behavior are observed and current
reversals can also be induced. These current reversals persist even for the
overdamped dynamics of the particles. | cond-mat_stat-mech |
Avalanche dynamics in hierarchical fiber bundles: Heterogeneous materials are often organized in a hierarchical manner, where a
basic unit is repeated over multiple scales.The structure then acquires a
self-similar pattern. Examples of such structure are found in various
biological and synthetic materials. The hierarchical structure can have
significant consequences for the failure strength and the mechanical response
of such systems. Here we consider a fiber bundle model with hierarchical
structure and study the effect of the self-similar arrangement on the avalanche
dynamics exhibited by the model during the approach to failure. We show that
the failure strength of the model generally decreases in a hierarchical
structure, as opposed to the situation where no such hierarchy exists. However,
we also report a special arrangement of the hierarchy for which the failure
threshold could be substantially above that of a non hierarchical reference
structure. | cond-mat_stat-mech |
Diffusion in Curved Spacetimes: Using simple kinematical arguments, we derive the Fokker-Planck equation for
diffusion processes in curved spacetimes. In the case of Brownian motion, it
coincides with Eckart's relativistic heat equation (albeit in a simpler form),
and therefore provides a microscopic justification for his phenomenological
heat-flux ansatz. Furthermore, we obtain the small-time asymptotic expansion of
the mean square displacement of Brownian motion in static spacetimes. Beyond
general relativity itself, this result has potential applications in analogue
gravitational systems. | cond-mat_stat-mech |
Fluctuation Relations For Adiabatic Pumping: We derive an extended fluctuation relation for an open system coupled with
two reservoirs under adiabatic one-cycle modulation. We confirm that the
geometric phase caused by the Berry-Sintisyn-Nemenman curvature in the
parameter space generates non-Gaussian fluctuations. This non-Gaussianity is
enhanced for the instantaneous fluctuation relation when the bias between the
two reservoirs disappears. | cond-mat_stat-mech |
Extracting Work from a single heat bath using velocity dependent
feedback: Thermodynamics of nanoscale devices is an active area of research. Despite
their noisy surround- ing they often produce mechanical work (e.g. micro-heat
engines) or display rectified Brownian motion (e.g. molecular motors). This
invokes the research in terms of experimentally quantifiable thermodynamic
efficiencies. To enhance the efficiency of such devices, close-loop control is
an useful technique. Here a single Brownian particle is driven by a harmonic
confinement with time-periodic contraction and expansion, together with a
velocity feedback that acts on the particle only when the trap contracts. Due
to this feedback we are able to extract thermodynamic work out of the system
having single heat bath without violating the Second Law of Thermodynamics. We
analyse the system using stochastic thermodynamics. | cond-mat_stat-mech |
Sensitivity to the initial conditions of the Time-Dependent Density
Functional Theory: Time-Dependent Density Functional Theory is mathematically formulated through
non-linear coupled time-dependent 3-dimensional partial differential equations
and it is natural to expect a strong sensitivity of its solutions to variations
of the initial conditions, akin to the butterfly effect ubiquitous in classical
dynamics. Since the Schr\"odinger equation for an interacting many-body system
is however linear and mathematically the exact equations of the Density
Functional Theory reproduce the corresponding one-body properties, it would
follow that the Lyapunov exponents are also vanishing within a Density
Functional Theory framework. Whether for realistic implementations of the
Time-Dependent Density Functional Theory the question of absence of the
butterfly effect and whether the dynamics provided is indeed a predictable
theory was never discussed. At the same time, since the time-dependent density
functional theory is a unique tool allowing us the study of non-equilibrium
dynamics of strongly interacting many-fermion systems, the question of
predictability of this theoretical framework is of paramount importance. Our
analysis, for a number of quantum superfluid many-body systems (unitary Fermi
gas, nuclear fission, and heavy-ion collisions) with a classical equivalent
number of degrees of freedom ${\cal O}(10^{10})$ and larger, suggests that its
maximum Lyapunov exponents are negligible for all practical purposes. | cond-mat_stat-mech |
On the entanglement entropy for a XY spin chain: The entanglement entropy for the ground state of a XY spin chain is related
to the corner transfer matrices of the triangular Ising model and expressed in
closed form. | cond-mat_stat-mech |
Connection Between Minimum of Solubility and Temperature of Maximum
Density in an Associating Lattice Gas Model: In this paper we investigate the solubility of a hard - sphere gas in a
solvent modeled as an associating lattice gas (ALG). The solution phase diagram
for solute at 5% is compared with the phase diagram of the original solute free
model. Model properties are investigated thr ough Monte Carlo simulations and a
cluster approximation. The model solubility is computed via simulations and
shown to exhibit a minimum as a function of temperature. The line of minimum
solubility (TmS) coincides with the line of maximum density (TMD) for different
solvent chemical potentials. | cond-mat_stat-mech |
Dynamics and thermodynamics of a topological transition in spin ice
materials under strain: We study single crystals of Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ under
magnetic field and stress applied along their [001] direction. We find that
many of the features that the emergent gauge field of spin ice confers to the
macroscopic magnetic properties are preserved in spite of the finite
temperature. The magnetisation vs. field shows an upward convexity within a
broad range of fields, while the static and dynamic susceptibilities present a
peculiar peak. Following this feature for both compounds, we determine a single
experimental transition curve: that for the Kasteleyn transition in three
dimensions, proposed more than a decade ago. Additionally, we observe that
compression up to $-0.8\%$ along [001] does not significantly change the
thermodynamics. However, the dynamical response of Ho$_2$Ti$_2$O$_7$ is quite
sensitive to changes introduced in the ${\rm Ho}^{3+}$ environment. Uniaxial
compression can thus open up experimental access to equilibrium properties of
spin ice at low temperatures. | cond-mat_stat-mech |
Realization of Levy flights as continuous processes: On the basis of multivariate Langevin processes we present a realization of
Levy flights as a continuous process. For the simple case of a particle moving
under the influence of friction and a velocity dependent stochastic force we
explicitly derive the generalized Langevin equation and the corresponding
generalized Fokker-Planck equation describing Levy flights. Our procedure is
similar to the treatment of the Kramers-Fokker Planck equation in the
Smoluchowski limit. The proposed approach forms a feasible way of tackling Levy
flights in inhomogeneous media or systems with boundaries what is up to now a
challenging problem. | cond-mat_stat-mech |
Some Finite Size Effects in Simulations of Glass Dynamics: We present the results of a molecular dynamics computer simulation in which
we investigate the dynamics of silica. By considering different system sizes,
we show that in simulations of the dynamics of this strong glass former
surprisingly large finite size effects are present. In particular we
demonstrate that the relaxation times of the incoherent intermediate scattering
function and the time dependence of the mean squared displacement are affected
by such finite size effects. By compressing the system to high densities, we
transform it to a fragile glass former and find that for that system these
types of finite size effects are much weaker. | cond-mat_stat-mech |
On the Conversion of Work into Heat: Microscopic Models and Macroscopic
Equations: We summarize and extend some of the results obtained recently for the
microscopic and macroscopic behavior of a pinned harmonic chain, with random
velocity flips at Poissonian times, acted on by a periodic force {at one end}
and in contact with a heat bath at the other end. Here we consider the case
where the system is in contact with two heat baths at different temperatures
and a periodic force is applied at any position. This leads in the hydrodynamic
limit to a heat equation for the temperature profile with a discontinuous slope
at the position where the force acts. Higher dimensional systems, unpinned
cases and anharmonic interactions are also considered. | cond-mat_stat-mech |
Phonon Thermodynamics versus Electron-Phonon Models: Applying the path integral formalism we study the equilibrium thermodynamics
of the phonon field both in the Holstein and in the Su-Schrieffer-Heeger
models. The anharmonic cumulant series, dependent on the peculiar source
currents of the {\it e-ph} models, have been computed versus temperature in the
case of a low energy oscillator. The cutoff in the series expansion has been
determined, in the low $T$ limit, using the constraint of the third law of
thermodynamics. In the Holstein model, the free energy derivatives do not show
any contribution ascribable to {\it e-ph} anharmonic effect. We find signatures
of large {\it e-ph} anharmonicities in the Su-Schrieffer-Heeger model mainly
visible in the temperature dependent peak displayed by the phonon heat
capacity. | cond-mat_stat-mech |
Counting metastable states in a kinetically constrained model using a
patch repetition analysis: We analyse metastable states in the East model, using a recently-proposed
patch-repetition analysis based on time-averaged density profiles. The results
reveal a hierarchy of states of varying lifetimes, consistent with previous
studies in which the metastable states were identified and used to explain the
glassy dynamics of the model. We establish a mapping between these states and
configurations of systems of hard rods, which allows us to analyse both typical
and atypical metastable states. We discuss connections between the complexity
of metastable states and large-deviation functions of dynamical quantities,
both in the context of the East model and more generally in glassy systems. | cond-mat_stat-mech |
Conservation-laws-preserving algorithms for spin dynamics simulations: We propose new algorithms for numerical integration of the equations of
motion for classical spin systems with fixed spatial site positions. The
algorithms are derived on the basis of a mid-point scheme in conjunction with
the multiple time staging propagation. Contrary to existing predictor-corrector
and decomposition approaches, the algorithms introduced preserve all the
integrals of motion inherent in the basic equations. As is demonstrated for a
lattice ferromagnet model, the present approach appears to be more efficient
even over the recently developed decomposition method. | cond-mat_stat-mech |
Criticality and self-organization in branching processes: application to
natural hazards: The statistics of natural catastrophes contains very counter-intuitive
results. Using earthquakes as a working example, we show that the energy
radiated by such events follows a power-law or Pareto distribution. This means,
in theory, that the expected value of the energy does not exist (is infinite),
and in practice, that the mean of a finite set of data in not representative of
the full population. Also, the distribution presents scale invariance, which
implies that it is not possible to define a characteristic scale for the
energy. A simple model to account for this peculiar statistics is a branching
process: the activation or slip of a fault segment can trigger other segments
to slip, with a certain probability, and so on. Although not recognized
initially by seismologists, this is a particular case of the stochastic process
studied by Galton and Watson one hundred years in advance, in order to model
the extinction of (prominent) families. Using the formalism of probability
generating functions we will be able to derive, in an accessible way, the main
properties of these models. Remarkably, a power-law distribution of energies is
only recovered in a very special case, when the branching process is at the
onset of attenuation and intensification, i.e., at criticality. In order to
account for this fact, we introduce the self-organized critical models, in
which, by means of some feedback mechanism, the critical state becomes an
attractor in the evolution of such systems. Analogies with statistical physics
are drawn. The bulk of the material presented here is self-contained, as only
elementary probability and mathematics are needed to start to read. | cond-mat_stat-mech |
Mechanisms of Granular Spontaneous Stratification and Segregation in
Two-Dimensional Silos: Spontaneous stratification of granular mixtures has been reported by Makse et
al. [Nature 386, 379 (1997)] when a mixture of grains differing in size and
shape is poured in a quasi-two-dimensional heap. We study this phenomenon using
two different approaches. First, we introduce a cellular automaton model that
illustrates clearly the physical mechanism; the model displays stratification
whenever the large grains are rougher than the small grains, in agreement with
the experiments. Moreover, the dynamics are close to those of the experiments,
where the layers are built through a ``kink'' at which the rolling grains are
stopped. Second, we develop a continuum approach, based on a recently
introduced set of coupled equations for surface flows of granular mixtures that
allows us to make quantitative predictions for relevant quantities. We study
the continuum model in two limit regimes: the large flux or thick flow regime,
where the percolation effect (i.e., segregation of the rolling grains in the
flow) is important, and the small flux or thin flow regime, where all the
rolling grains are in contact with the surface of the sandpile. We find that
the wavelength of the layers behaves linearly with the flux of grains. We
obtain analytical predictions for the shape of the kink giving rise to
stratification as well as the profile of the rolling and static species when
segregation of the species is observed. | cond-mat_stat-mech |
Classical no-cloning theorem under Liouville dynamics by non-Csiszár
f-divergence: The Csisz\'ar f-divergence, which is a class of information distances, is
known to offer a useful tool for analysing the classical counterpart of the
cloning operations that are quantum mechanically impossible for the factorized
and marginality classical probability distributions under Liouville dynamics.
We show that a class of information distances that does not belong to this
divergence class also allows for the formulation of a classical analogue of the
quantum no-cloning theorem. We address a family of nonlinear Liouville-like
equations, and generic distances, to obtain constraints on the corresponding
functional forms, associated with the formulation of classical analogue of the
no-cloning principle. | cond-mat_stat-mech |
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