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Stochastic model of self-driven two-species objects in the context of
the pedestrian dynamics: In this work we propose a model to describe the statistical fluctuations of
the self-driven objects (species A) walking against an opposite crowd (species
B) in order to simulate the regime characterized by stop-and-go waves in the
context of pedestrian dynamics. By using the concept of single-biased random
walks (SBRW), this setup is modeled both via partial differential equations and
by Monte-Carlo simulations. The problem is non-interacting until the opposite
particles visit the same cell of the considered particle. In this situation,
delays on the residence time of the particles per cell depends on the
concentration of particles of opposite species. We analyzed the fluctuations on
the position of particles and our results show a non-regular diffusion
characterized by long-tailed and asymmetric distributions which is better
fitted by some chromatograph distributions found in the literature. We also
show that effects of the reverse crowd particles is able to enlarge the
dispersion of target particles in relation to the non-biased case ($\alpha =0$)
after observing a small decrease of this dispersion | cond-mat_stat-mech |
Hidden slow degrees of freedom and fluctuation theorems: an analytically
solvable model: In some situations in stochastic thermodynamics not all relevant slow degrees
of freedom are accessible. Consequently, one adopts an effective description
involving only the visible degrees of freedom. This gives rise to an apparent
entropy production that violates standard fluctuation theorems. We present an
analytically solvable model illustrating how the fluctuation theorems are
modified. Furthermore, we define an alternative to the apparent entropy
production: the marginal entropy production which fulfills the fluctuation
theorems in the usual form. We show that the non-Markovianity of the visible
process is responsible for the deviations in the fluctuation theorems. | cond-mat_stat-mech |
Mapping a Homopolymer onto a Model Fluid: We describe a linear homopolymer using a Grand Canonical ensemble formalism,
a statistical representation that is very convenient for formal manipulations.
We investigate the properties of a system where only next neighbor interactions
and an external, confining, field are present, and then show how a general pair
interaction can be introduced perturbatively, making use of a Mayer expansion.
Through a diagrammatic analysis, we shall show how constitutive equations
derived for the polymeric system are equivalent to the Ornstein-Zernike and
P.Y. equations for a simple fluid, and find the implications of such a mapping
for the simple situation of Van der Waals mean field model for the fluid. | cond-mat_stat-mech |
From crystal to amorphopus: a novel route towards unjamming in soft disk
packings: It is presented a numerical study on the unjamming packing fraction of bi-
and polydisperse disk packings, which are generated through compression of a
monodisperse crystal. In bidisperse systems, a fraction f_+ = 40% up to 80% of
the total number of particles have their radii increased by \Delta R, while the
rest has their radii decreased by the same amount. Polydisperse packings are
prepared by changing all particle radii according to a uniform distribution in
the range [-\Delta R,\Delta R]. The results indicate that the critical packing
fraction is never larger than the value for the initial monodisperse crystal,
\phi = \pi/12, and that the lowest value achieved is approximately the one for
random close packing. These results are seen as a consequence of the interplay
between the increase in small-small particle contacts and the local crystalline
order provided by the large-large particle contacts. | cond-mat_stat-mech |
On the universal Gaussian behavior of Driven Lattice Gases at
short-times: The dynamic and static critical behaviors of driven and equilibrium lattice
gas models are studied in two spatial dimensions. We show that in the
short-time regime immediately following a critical quench, the dynamics of the
transverse order parameters, auto-correlations, and Binder cumulant are
consistent with the prediction of a Gaussian, $i.e.,$ non-interacting,
effective theory, both for the equilibrium lattice gas and its nonequilibrium
counterparts. Such a "super-universal" behavior is observed only at short times
after a critical quench, while the various models display their distinct
behaviors in the stationary states, described by the corresponding, known
universality classes. | cond-mat_stat-mech |
Quasiperiodicity in the $α-$Fermi-Pasta-Ulam-Tsingou problem
revisited: an approach using ideas from wave turbulence: The Fermi-Pasta-Ulam-Tsingou (FPUT) problem addresses fundamental questions
in statistical physics, and attempts to understand the origin of recurrences in
the system have led to many great advances in nonlinear dynamics and
mathematical physics. In this work we revisit the problem and study
quasiperiodic recurrences in the weakly nonlinear $\alpha-$FPUT system in more
detail. We aim to reconstruct the quasiperiodic behaviour observed in the
original paper from the canonical transformation used to remove the three wave
interactions, which is necessary before applying the wave turbulence formalism.
We expect the construction to match the observed quasiperiodicity if we are in
the weakly nonlinear regime. Surprisingly, in our work we show that this is not
always the case and in particular, the recurrences observed in the original
paper cannot be constructed by our method. We attribute this disagreement to
the presence of small denominators in the canonical transformation used to
remove the three wave interactions before arriving at the starting point of
wave turbulence. We also show that these small denominators are present even in
the weakly nonlinear regime, and they become more significant as the system
size is increased. We also discuss our results in the context of the problem of
equilibration in the $\alpha-$FPUT system, and point out some mathematical
challenges when the wave turbulence formalism is applied to explain
thermalization in the $\alpha-$FPUT problem. We argue that certain aspects of
the $\alpha-$FPUT system such as presence of the stochasticity threshold,
thermalization in the thermodynamic limit and the cause of quasiperiodicity are
not clear, and that they require further mathematical and numerical studies. | cond-mat_stat-mech |
Peierls instability for the Holstein model: We consider the static Holstein model, describing a chain of Fermions
interacting with a classical phonon field, when the interaction is weak and the
density is a rational number. We show that the energy of the system, as a
function of the phonon field, has two stationary points, defined up to a
lattice translation, which are local minima in the space of fields periodic
with period equal to the inverse of the density. | cond-mat_stat-mech |
Power-Law Time Distribution of Large Earthquakes: We study the statistical properties of time distribution of seimicity in
California by means of a new method of analysis, the Diffusion Entropy. We find
that the distribution of time intervals between a large earthquake (the main
shock of a given seismic sequence) and the next one does not obey Poisson
statistics, as assumed by the current models. We prove that this distribution
is an inverse power law with an exponent $\mu=2.06 \pm 0.01$. We propose the
Long-Range model, reproducing the main properties of the diffusion entropy and
describing the seismic triggering mechanisms induced by large earthquakes. | cond-mat_stat-mech |
Understanding how both the partitions of a bipartite network affect its
one-mode projection: It is a well-known fact that the degree distribution (DD) of the nodes in a
partition of a bipartite network influences the DD of its one-mode projection
on that partition. However, there are no studies exploring the effect of the DD
of the other partition on the one-mode projection. In this article, we show
that the DD of the other partition, in fact, has a very strong influence on the
DD of the one-mode projection. We establish this fact by deriving the exact or
approximate closed-forms of the DD of the one-mode projection through the
application of generating function formalism followed by the method of
iterative convolution. The results are cross-validated through appropriate
simulations. | cond-mat_stat-mech |
Understanding the Frequency Distribution of Mechanically Stable Disk
Packings: Relative frequencies of mechanically stable (MS) packings of frictionless
bidisperse disks are studied numerically in small systems. The packings are
created by successively compressing or decompressing a system of soft purely
repulsive disks, followed by energy minimization, until only infinitesimal
particle overlaps remain. For systems of up to 14 particles most of the MS
packings were generated. We find that the packings are not equally probable as
has been assumed in recent thermodynamic descriptions of granular systems.
Instead, the frequency distribution, averaged over each packing-fraction
interval $\Delta \phi$, grows exponentially with increasing $\phi$. Moreover,
within each packing-fraction interval MS packings occur with frequencies $f_k$
that differ by many orders of magnitude. Also, key features of the frequency
distribution do not change when we significantly alter the packing-generation
algorithm--for example frequent packings remain frequent and rare ones remain
rare. These results indicate that the frequency distribution of MS packings is
strongly influenced by geometrical properties of the multidimensional
configuration space. By adding thermal fluctuations to a set of the MS
packings, we were able to examine a number of local features of configuration
space near each packing including the time required for a given packing to
break to a distinct one, which enabled us to estimate the energy barriers that
separate one packing from another. We found a positive correlation between the
packing frequencies and the heights of the lowest energy barriers $\epsilon_0$.
We also examined displacement fluctuations away from the MS packings to
correlate the size and shape of the local basins near each packing to the
packing frequencies. | cond-mat_stat-mech |
Relaxation of nonequilibrium populations after a pump: the breaking of
Mathiessen$'$s rule: From the early days of many-body physics, it was realized that the
self-energy governs the relaxation or lifetime of the retarded Green$'$s
function. So it seems reasonable to directly extend those results into the
nonequilibrium domain. But experiments and calculations of the response of
quantum materials to a pump show that the relationship between the relaxation
and the self-energy only holds in special cases. Experimentally, the decay time
for a population to relax back to equilibrium and the linewidth measured in a
linear-response angle-resolved photoemission spectroscopy differ by large
amounts. Theoretically, aside from the weak-coupling regime where the
relationship holds, one also finds deviations and additionally one sees
violations of Mathiessen$'$s rule. In this work, we examine whether looking at
an effective transport relaxation time helps to analyze the decay times of
excited populations as they relax back to equilibrium. We conclude that it may
do a little better, but it has a fitting parameter for the overall scale which
must be determined. | cond-mat_stat-mech |
First-passage and extreme-value statistics of a particle subject to a
constant force plus a random force: We consider a particle which moves on the x axis and is subject to a constant
force, such as gravity, plus a random force in the form of Gaussian white
noise. We analyze the statistics of first arrival at point $x_1$ of a particle
which starts at $x_0$ with velocity $v_0$. The probability that the particle
has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival,
and the velocity distribution at first arrival are all considered. We also
study the statistics of the first return of the particle to its starting point.
Finally, we point out that the extreme-value statistics of the particle and the
first-passage statistics are closely related, and we derive the distribution of
the maximum displacement $m={\rm max}_t[x(t)]$. | cond-mat_stat-mech |
Persistence discontinuity in disordered contact processes with
long-range interactions: We study the local persistence probability during non-stationary time
evolutions in disordered contact processes with long-range interactions by a
combination of the strong-disorder renormalization group (SDRG) method, a
phenomenological theory of rare regions, and numerical simulations. We find
that, for interactions decaying as an inverse power of the distance, the
persistence probability tends to a non-zero limit not only in the inactive
phase but also in the critical point. Thus, unlike in the contact process with
short-range interactions, the persistence in the limit $t\to\infty$ is a
discontinuous function of the control parameter. For stretched exponentially
decaying interactions, the limiting value of the persistence is found to remain
continuous, similar to the model with short-range interactions. | cond-mat_stat-mech |
Theoretical construction of 1D anyon models: One-dimensional anyon models are renewedly constructed by using path integral
formalism. A statistical interaction term is introduced to realize the anyonic
exchange statistics. The quantum mechanics formulation of statistical
transmutation is presented. | cond-mat_stat-mech |
Transient anomalous diffusion in heterogeneous media with stochastic
resetting: We investigate a diffusion process in heterogeneous media where particles
stochastically reset to their initial positions at a constant rate. The
heterogeneous media is modeled using a spatial-dependent diffusion coefficient
with a power-law dependence on particles' positions. We use the Green function
approach to obtain exact solutions for the probability distribution of
particles' positions and the mean square displacement. These results are
further compared and agree with numerical simulations of a Langevin equation.
We also study the first-passage time problem associated with this diffusion
process and obtain an exact expression for the mean first-passage time. Our
findings show that this system exhibits non-Gaussian distributions, transient
anomalous diffusion (sub- or superdiffusion) and stationary states that
simultaneously depend on the media heterogeneity and the resetting rate. We
further demonstrate that the media heterogeneity non-trivially affect the mean
first-passage time, yielding an optimal resetting rate for which this quantity
displays a minimum. | cond-mat_stat-mech |
Analytic model of thermalization: Quantum emulation of classical
cellular automata: We introduce a novel method of quantum emulation of a classical reversible
cellular automaton. By applying this method to a chaotic cellular automaton,
the obtained quantum many-body system thermalizes while all the energy
eigenstates and eigenvalues are solvable. These explicit solutions allow us to
verify the validity of some scenarios of thermalization to this system. We find
that two leading scenarios, the eigenstate thermalization hypothesis scenario
and the large effective dimension scenario, do not explain thermalization in
this model. | cond-mat_stat-mech |
Hidden Criticality of Counterion Condensation Near a Charged Cylinder: We study the condensation transition of counterions on a charged cylinder via
Monte Carlo simulations. Varying the cylinder radius systematically in relation
to the system size, we find that all counterions are bound to the cylinder and
the heat capacity shows a drop at a finite Manning parameter. A finite-size
scaling analysis is carried out to confirm the criticality of the complete
condensation transition, yielding the same critical exponents with the Manning
transition. We show that the existence of the complete condensation is
essential to explain how the condensation nature alters from continuous to
discontinuous transition. | cond-mat_stat-mech |
Microscopic theory of the glassy dynamics of passive and active network
materials: Signatures of glassy dynamics have been identified experimentally for a rich
variety of materials in which molecular networks provide rigidity. Here we
present a theoretical framework to study the glassy behavior of both passive
and active network materials. We construct a general microscopic network model
that incorporates nonlinear elasticity of individual filaments and steric
constraints due to crowding. Based on constructive analogies between structural
glass forming liquids and random field Ising magnets implemented using a
heterogeneous self-consistent phonon method, our scheme provides a microscopic
approach to determine the mismatch surface tension and the configurational
entropy, which compete in determining the barrier for structural rearrangements
within the random first order transition theory of escape from a local energy
minimum. The influence of crosslinking on the fragility of inorganic network
glass formers is recapitulated by the model. For active network materials, the
mapping, which correlates the glassy characteristics to the network
architecture and properties of nonequilibrium motor processes, is shown to
capture several key experimental observations on the cytoskeleton of living
cells: Highly connected tense networks behave as strong glass formers; intense
motor action promotes reconfiguration. The fact that our model assuming a
negative motor susceptibility predicts the latter suggests that on average the
motorized processes in living cells do resist the imposed mechanical load. Our
calculations also identify a spinodal point where simultaneously the mismatch
penalty vanishes and the mechanical stability of amorphous packing disappears. | cond-mat_stat-mech |
Hidden slow degrees of freedom and fluctuation theorems: an analytically
solvable model: In some situations in stochastic thermodynamics not all relevant slow degrees
of freedom are accessible. Consequently, one adopts an effective description
involving only the visible degrees of freedom. This gives rise to an apparent
entropy production that violates standard fluctuation theorems. We present an
analytically solvable model illustrating how the fluctuation theorems are
modified. Furthermore, we define an alternative to the apparent entropy
production: the marginal entropy production which fulfills the fluctuation
theorems in the usual form. We show that the non-Markovianity of the visible
process is responsible for the deviations in the fluctuation theorems. | cond-mat_stat-mech |
The second law and fluctuations of work: The case against quantum
fluctuation theorems: We study how Thomson's formulation of the second law: no work is extracted
from an equilibrium ensemble by a cyclic process, emerges in the quantum
situation through the averaging over fluctuations of work. The latter concept
is carefully defined for an ensemble of quantum systems interacting with
macroscopic sources of work. The approach is based on first splitting a mixed
quantum ensemble into pure subensembles, which according to quantum mechanics
are maximally complete and irreducible. The splitting is done by filtering the
outcomes of a measurement process. A critical review is given of two other
approaches to fluctuations of work proposed in the literature. It is shown that
in contrast to those ones, the present definition {\it i)} is consistent with
the physical meaning of the concept of work as mechanical energy lost by the
macroscopic sources, or, equivalently, as the average energy acquired by the
ensemble; {\it ii)} applies to an arbitrary non-equilibrium state. There is no
direct generalization of the classical work-fluctuation theorem to the proper
quantum domain. This implies some non-classical scenarios for the emergence of
the second law. | cond-mat_stat-mech |
Nucleation of Market Shocks in Sornette-Ide model: The Sornette-Ide differential equation of herding and rational trader
behaviour together with very small random noise is shown to lead to crashes or
bubbles where the price change goes to infinity after an unpredictable time.
About 100 time steps before this singularity, a few predictable roughly
log-periodic oscillations are seen. | cond-mat_stat-mech |
Efficient stochastic thermostatting of path integral molecular dynamics: The path integral molecular dynamics (PIMD) method provides a convenient way
to compute the quantum mechanical structural and thermodynamic properties of
condensed phase systems at the expense of introducing an additional set of
high-frequency normal modes on top of the physical vibrations of the system.
Efficiently sampling such a wide range of frequencies provides a considerable
thermostatting challenge. Here we introduce a simple stochastic path integral
Langevin equation (PILE) thermostat which exploits an analytic knowledge of the
free path integral normal mode frequencies. We also apply a recently-developed
colored-noise thermostat based on a generalized Langevin equation (GLE), which
automatically achieves a similar, frequency-optimized sampling. The sampling
efficiencies of these thermostats are compared with that of the more
conventional Nos\'e-Hoover chain (NHC) thermostat for a number of physically
relevant properties of the liquid water and hydrogen-in-palladium systems. In
nearly every case, the new PILE thermostat is found to perform just as well as
the NHC thermostat while allowing for a computationally more efficient
implementation. The GLE thermostat also proves to be very robust delivering a
near-optimum sampling efficiency in all of the cases considered. We suspect
that these simple stochastic thermostats will therefore find useful application
in many future PIMD simulations. | cond-mat_stat-mech |
3-Dimensional Multilayered 6-vertex Statistical Model: Exact Solution: Solvable via Bethe Ansatz (BA) anisotropic statistical model on cubic lattice
consisting of locally interacting 6-vertex planes, is studied. Symmetries of BA
lead to infinite hierarchy of possible phases, which is further restricted by
numerical simulations. The model is solved for arbitrary value of the
interlayer coupling constant. Resulting is the phase diagram in general
3-parameter space. Exact mapping onto the models with some inhomogenious sets
of interlayer coupling constants is established. | cond-mat_stat-mech |
Equivalent-neighbor Potts models in two dimensions: We investigate the two-dimensional $q=3$ and 4 Potts models with a variable
interaction range by means of Monte Carlo simulations. We locate the phase
transitions for several interaction ranges as expressed by the number $z$ of
equivalent neighbors. For not too large $z$, the transitions fit well in the
universality classes of the short-range Potts models. However, at longer ranges
the transitions become discontinuous. For $q=3$ we locate a tricritical point
separating the continuous and discontinuous transitions near $z=80$, and a
critical fixed point between $z=8$ and 12. For $q=4$ the transition becomes
discontinuous for $z > 16$. The scaling behavior of the $q=4$ model with $z=16$
approximates that of the $q=4$ merged critical-tricritical fixed point
predicted by the renormalization scenario. | cond-mat_stat-mech |
Efficient Simulation of Low Temperature Physics in One-Dimensional
Gapless Systems: We discuss the computational efficiency of the finite temperature simulation
with the minimally entangled typical thermal states (METTS). To argue that
METTS can be efficiently represented as matrix product states, we present an
analytic upper bound for the average entanglement Renyi entropy of METTS for
Renyi index $0<q\leq 1$. In particular, for 1D gapless systems described by
CFTs, the upper bound scales as $\mathcal{O}(c N^0 \log \beta)$ where $c$ is
the central charge and $N$ is the system size. Furthermore, we numerically find
that the average Renyi entropy exhibits a universal behavior characterized by
the central charge and is roughly given by half of the analytic upper bound.
Based on these results, we show that METTS provide a significant speedup
compared to employing the purification method to analyze thermal equilibrium
states at low temperatures in 1D gapless systems. | cond-mat_stat-mech |
Cutting-Plane Algorithms and Solution Whitening for the Vertex-Cover
Problem: The phase-transition behavior of the NP-hard vertex-cover (VC) combinatorial
optimization problem is studied numerically by linear programming (LP) on
ensembles of random graphs. As the basic Simplex (SX) algorithm suitable for
such LPs may produce incomplete solutions for sufficiently complex graphs, the
application of cutting-plane (CP) methods is sought. We consider Gomory and
{0,1/2} cuts. We measure the probability of obtaining complete solutions with
these approaches as a function of the average node degree c and observe
transition between typically complete and incomplete phase regions. While not
generally complete solutions are obtained for graphs of arbitrarily high
complexity, the CP approaches still advance the boundary in comparison to the
pure SX algorithm, beyond the known replica-symmetry breaking (RSB) transition
at c=e=2.718... . In fact, our results provide evidence for another algorithmic
transition at c=2.90(2).
Besides this, we quantify the transition between easy and hard solvability of
the VC problem also in terms of numerical effort. Further we study the
so-called whitening of the solution, which is a measure for the degree of
freedom that single vertices experience with respect to degenerate solutions.
Inspection of the quantities related to clusters of white vertices reveals that
whitening is affected, only slightly but measurably, by the RSB transition. | cond-mat_stat-mech |
Random walks in unweighted and weighted modular scale-free networks with
a perfect trap: Designing optimal structure favorable to diffusion and effectively
controlling the trapping process are crucial in the study of trapping
problem---random walks with a single trap. In this paper, we study the trapping
problem occurring on unweighted and weighted networks, respectively. The
networks under consideration display the striking scale-free, small-world, and
modular properties, as observed in diverse real-world systems. For binary
networks, we concentrate on three cases of trapping problems with the trap
located at a peripheral node, a neighbor of the root with the least
connectivity, and a farthest node, respectively. For weighted networks with
edge weights controlled by a parameter, we also study three trapping problems,
in which the trap is placed separately at the root, a neighbor of the root with
the least degree, and a farthest node. For all the trapping problems, we obtain
the analytical formulas for the average trapping time (ATT) measuring the
efficiency of the trapping process, as well as the leading scaling of ATT. We
show that for all the trapping problems in the binary networks with a trap
located at different nodes, the dominating scalings of ATT reach the possible
minimum scalings, implying that the networks have optimal structure that is
advantageous to efficient trapping. Furthermore, we show that for trapping in
the weighted networks, the ATT is controlled by the weight parameter, through
modifying which, the ATT can behave superlinealy, linearly, sublinearly, or
logarithmically with the system size. This work could help improving the design
of systems with efficient trapping process and offers new insight into control
of trapping in complex systems. | cond-mat_stat-mech |
Exact results for a generalized spin-1/2 Ising-Heisenberg diamond chain
with the second-neighbor interaction between nodal spins: The ground state and thermodynamics of a generalized spin-1/2
Ising-Heisenberg diamond chain with the second-neighbor interaction between
nodal spins are calculated exactly using the mapping method based on the
decoration-iteration transformation. Rigorous results for the magnetization,
susceptibility, and heat capacity are investigated in dependence on temperature
and magnetic field for the frustrated diamond spin chain with the
antiferromagnetic Ising and Heisenberg interactions. It is demonstrated that
the second-neighbor interaction between nodal spins gives rise to a greater
diversity of low-temperature magnetization curves, which may include an
intermediate plateau at two-third of the saturation magnetization related to
the classical ferrimagnetic (up-up-up-down-up-up-...) ground state with
translationally broken symmetry besides an intermediate one-third magnetization
plateau reflecting the translationally invariant quantum ferrimagnetic
(monomer-dimer) spin arrangement. | cond-mat_stat-mech |
Enhancement of stability of metastable states in the presence of
Lévy noise: The barrier crossing event for superdiffusion in the form of symmetric
L\'{e}vy flights is investigated. We derive from the fractional Fokker-Planck
equation a general differential equation with the corresponding conditions
useful to calculate the mean residence time of a particle in a fixed interval
for an arbitrary smooth potential profile, in particular metastable, with a
sink and a L\'{e}vy noise with an arbitrary index $\alpha$. A closed expression
in quadrature of the nonlinear relaxation time for L\'{e}vy flights with the
index $\alpha =1$ in cubic metastable potential is obtained. Enhancement of the
mean residence time in the metastable state, analytically derived, due to
L\'{e}vy noise is found. | cond-mat_stat-mech |
Resonant suppression of thermal stability of the nanoparticle
magnetization by a rotating magnetic field: We study the thermal stability of the periodic (P) and quasi-periodic (Q)
precessional modes of the nanoparticle magnetic moment induced by a rotating
magnetic field. An analytical method for determining the lifetime of the P mode
in the case of high anisotropy barrier and small amplitudes of the rotating
field is developed within the Fokker-Planck formalism. In general case, the
thermal stability of both P and Q modes is investigated by numerical simulation
of the stochastic Landau-Lifshitz equation. We show analytically and
numerically that the lifetime is a nonmonotonic function of the rotating field
frequency which, depending on the direction of field rotation, has either a
pronounced maximum or a deep minimum near the Larmor frequency. | cond-mat_stat-mech |
Anomalous Behavior of the Zero Field Susceptibility of the Ising Model
on the Cayley Tree: It is found that the zero field susceptibility chi of the Ising model on the
Cayley tree exhibits unusually weak divergence at the critical point Tc. The
susceptibility amplitude is found to diverge at Tc proportionally to the tree
generation level n, while the behavior of chi is otherwise analytic in the
vicinity of Tc, with the critical exponent gamma=0. | cond-mat_stat-mech |
The Thermodynamic Casimir Effect in $^4$He Films near $T_λ$: Monte
Carlo Results: The universal finite-size scaling function of the critical Casimir force for
the three dimensional XY universality class with Dirichlet boundary conditions
is determined using Monte Carlo simulations. The results are in excellent
agreement with recent experiments on $^4$He Films at the superfluid transition
and with available theoretical predictions. | cond-mat_stat-mech |
Driving, conservation and absorbing states in sandpiles: We use a phenomenological field theory, reflecting the symmetries and
conservation laws of sandpiles, to compare the driven dissipative sandpile,
widely studied in the context of self-organized criticality, with the
corresponding fixed-energy model. The latter displays an absorbing-state phase
transition with upper critical dimension $d_c=4$. We show that the driven model
exhibits a fundamentally different approach to the critical point, and compute
a subset of critical exponents. We present numerical simulations in support of
our theoretical predictions. | cond-mat_stat-mech |
Stable quasicrystalline ground states: We give a strong evidence that noncrystalline materials such as quasicrystals
or incommensurate solids are not exceptions but rather are generic in some
regions of a phase space. We show this by constructing classical lattice-gas
models with translation-invariant, finite-range interactions and with a unique
quasiperiodic ground state which is stable against small perturbations of
two-body potentials. More generally, we provide a criterion for stability of
nonperiodic ground states. | cond-mat_stat-mech |
Fixation in cyclically competing species on a directed graph with
quenched disorder: A simple model of cyclically competing species on a directed graph with
quenched disorder is proposed as an extension of the rock-paper-scissors model.
By assuming that the effects of loops in a directed random graph can be ignored
in the thermodynamic limit, it is proved for any finite disorder that the
system fixates to a frozen configuration when the species number $s$ is larger
than the spatial connectivity $c$, and otherwise stays active. Nontrivial lower
and upper bounds for the persistence probability of a site never changing its
state are also analytically computed. The obtained bounds and numerical
simulations support the existence of a phase transition as a function of
disorder for $1<c_l(s)\le c <s$, with a $s$-dependent threshold of the
connectivity $c_l(s)$. | cond-mat_stat-mech |
Thermodynamics of the mesoscopic thermoelectric heat engine beyond the
linear-response regime: Mesoscopic thermoelectric heat engine is much anticipated as a device that
allows us to utilize with high efficiency wasted heat inaccessible by
conventional heat engines. However, the derivation of the heat current in this
engine seems to be either not general or described too briefly, even
inappropriate in some cases. In this paper, we give a clear-cut derivation of
the heat current of the engine with suitable assumptions beyond the
linear-response regime. It resolves the confusion in the definition of the heat
current in the linear-response regime. After verifying that we can construct
the same formalism as that of the cyclic engine, we find the following two
interesting results within the Landauer-B\"uttiker formalism: the efficiency of
the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only
if the transmission probability is finite at a specific energy and zero
otherwise; the unitarity of the transmission probability guarantees the second
law of thermodynamics, invalidating Benenti et al.'s argument in the
linear-response regime that one could obtain a finite power with the Carnot
efficiency under a broken time-reversal symmetry. These results demonstrate how
quantum mechanics constraints thermodynamics. | cond-mat_stat-mech |
Diffusion-limited reactions in dynamic heterogeneous media: Most biochemical reactions in living cells rely on diffusive search for
target molecules or regions in a heterogeneous overcrowded cytoplasmic medium.
Rapid re-arrangements of the medium constantly change the effective diffusivity
felt locally by a diffusing particle and thus impact the distribution of the
first-passage time to a reaction event. Here, we investigate the effect of
these dynamic spatio-temporal heterogeneities onto diffusion-limited reactions.
We describe a general mathematical framework to translate many results for
ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular,
we derive the probability density of the first-passage time to a reaction event
and show how the dynamic disorder broadens the distribution and increases the
likelihood of both short and long trajectories to reactive targets. While the
disorder slows down reaction kinetics on average, its dynamic character is
beneficial for a faster search and realization of an individual reaction event
triggered by a single molecule. | cond-mat_stat-mech |
Ferromagnetic ordering in graphs with arbitrary degree distribution: We present a detailed study of the phase diagram of the Ising model in random
graphs with arbitrary degree distribution. By using the replica method we
compute exactly the value of the critical temperature and the associated
critical exponents as a function of the minimum and maximum degree, and the
degree distribution characterizing the graph. As expected, there is a
ferromagnetic transition provided <k> <= <k^2> < \infty. However, if the fourth
moment of the degree distribution is not finite then non-trivial scaling
exponents are obtained. These results are analyzed for the particular case of
power-law distributed random graphs. | cond-mat_stat-mech |
Derivation and Improvements of the Quantum Canonical Ensemble from a
Regularized Microcanonical Ensemble: We develop a regularization of the quantum microcanonical ensemble, called a
Gaussian ensemble, which can be used for derivation of the canonical ensemble
from microcanonical principles. The derivation differs from the usual methods
by giving an explanation for the, at the first sight unreasonable,
effectiveness of the canonical ensemble when applied to certain small,
isolated, systems. This method also allows a direct identification between the
parameters of the microcanonical and the canonical ensemble and it yields
simple indicators and rigorous bounds for the effectiveness of the
approximation. Finally, we derive an asymptotic expansion of the microcanonical
corrections to the canonical ensemble for those systems, which are near, but
not quite, at the thermodynamical limit and show how and why the canonical
ensemble can be applied also for systems with exponentially increasing density
of states. The aim throughout the paper is to keep mathematical rigour intact
while attempting to produce results both physically and practically
interesting. | cond-mat_stat-mech |
Size effects on generation recombination noise: We carry out an analytical theory of generation-recombination noise for a two
level resistor model which goes beyond those presently available by including
the effects of both space charge fluctuations and diffusion current. Finite
size effects are found responsible for the saturation of the low frequency
current spectral density at high enough applied voltages. The saturation
behaviour is controlled essentially by the correlations coming from the long
range Coulomb interaction. It is suggested that the saturation of the current
fluctuations for high voltage bias constitutes a general feature of
generation-recombination noise. | cond-mat_stat-mech |
Canonical thermalization: For quantum systems that are weakly coupled to a much 'bigger' environment,
thermalization of possibly far from equilibrium initial ensembles is
demonstrated: for sufficiently large times, the ensemble is for all practical
purposes indistinguishable from a canonical density operator under conditions
that are satisfied under many, if not all, experimentally realistic conditions. | cond-mat_stat-mech |
Fluctuation-dissipation relations far from equilibrium: The fluctuation-dissipation (F-D) theorem is a fundamental result for systems
near thermodynamic equilibrium, and justifies studies between microscopic and
macroscopic properties. It states that the nonequilibrium relaxation dynamics
is related to the spontaneous fluctuation at equilibrium. Most processes in
Nature are out of equilibrium, for which we have limited theory. Common wisdom
believes the F-D theorem is violated in general for systems far from
equilibrium. Recently we show that dynamics of a dissipative system described
by stochastic differential equations can be mapped to that of a thermostated
Hamiltonian system, with a nonequilibrium steady state of the former
corresponding to the equilibrium state of the latter. Her we derived the
corresponding F-D theorem, and tested with several examples. We suggest further
studies exploiting the analogy between a general dissipative system appearing
in various science branches and a Hamiltonian system. Especially we discussed
the implications of this work on biological network studies. | cond-mat_stat-mech |
Fractional calculus and continuous-time finance II: the waiting-time
distribution: We complement the theory of tick-by-tick dynamics of financial markets based
on a Continuous-Time Random Walk (CTRW) model recently proposed by Scalas et
al., and we point out its consistency with the behaviour observed in the
waiting-time distribution for BUND future prices traded at LIFFE, London. | cond-mat_stat-mech |
Hybrid quantum-classical method for simulating high-temperature dynamics
of nuclear spins in solids: First-principles calculations of high-temperature spin dynamics in solids in
the context of nuclear magnetic resonance (NMR) is a long-standing problem,
whose conclusive solution can significantly advance the applications of NMR as
a diagnostic tool for material properties. In this work, we propose a new
hybrid quantum-classical method for computing NMR free induction decay(FID) for
spin $1/2$ lattices. The method is based on the simulations of a finite cluster
of spins $1/2$ coupled to an environment of interacting classical spins via a
correlation-preserving scheme. Such simulations are shown to lead to accurate
FID predictions for one-, two- and three-dimensional lattices with a broad
variety of interactions. The accuracy of these predictions can be efficiently
estimated by varying the size of quantum clusters used in the simulations. | cond-mat_stat-mech |
An information theory-based approach for optimal model reduction of
biomolecules: In the theoretical modelling of a physical system a crucial step consists in
the identification of those degrees of freedom that enable a synthetic, yet
informative representation of it. While in some cases this selection can be
carried out on the basis of intuition and experience, a straightforward
discrimination of the important features from the negligible ones is difficult
for many complex systems, most notably heteropolymers and large biomolecules.
We here present a thermodynamics-based theoretical framework to gauge the
effectiveness of a given simplified representation by measuring its information
content. We employ this method to identify those reduced descriptions of
proteins, in terms of a subset of their atoms, that retain the largest amount
of information from the original model; we show that these highly informative
representations share common features that are intrinsically related to the
biological properties of the proteins under examination, thereby establishing a
bridge between protein structure, energetics, and function. | cond-mat_stat-mech |
Level Set Percolation in Two-Dimensional Gaussian Free Field: The nature of level set percolation in the two-dimension Gaussian Free Field
has been an elusive question. Using a loop-model mapping, we show that there is
a nontrivial percolation transition, and characterize the critical point. In
particular, the correlation length diverges exponentially, and the critical
clusters are "logarithmic fractals", whose area scales with the linear size as
$A \sim L^2 / \sqrt{\ln L}$. The two-point connectivity also decays as the log
of the distance. We corroborate our theory by numerical simulations. Possible
CFT interpretations are discussed. | cond-mat_stat-mech |
Kardar-Parisi-Zhang universality in two-component driven diffusive
models: Symmetry and renormalization group perspectives: We elucidate the universal spatio-temporal scaling properties of the
time-dependent correlation functions in a class of two-component
one-dimensional (1D) driven diffusive system that consists of two coupled
asymmetric exclusion process. By using a perturbative renormalization group
framework, we show that the relevant scaling exponents have values same as
those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal
scaling exponents with the symmetries of the model equations. We thus establish
that these models belong to the 1D KPZ universality class. | cond-mat_stat-mech |
Statistical thermodynamics of a two dimensional relativistic gas: In this article we study a fully relativistic model of a two dimensional
hard-disk gas. This model avoids the general problems associated with
relativistic particle collisions and is therefore an ideal system to study
relativistic effects in statistical thermodynamics. We study this model using
molecular-dynamics simulation, concentrating on the velocity distribution
functions. We obtain results for $x$ and $y$ components of velocity in the rest
frame ($\Gamma$) as well as the moving frame ($\Gamma'$). Our results confirm
that J\"{u}ttner distribution is the correct generalization of
Maxwell-Boltzmann distribution. We obtain the same "temperature" parameter
$\beta$ for both frames consistent with a recent study of a limited
one-dimensional model. We also address the controversial topic of temperature
transformation. We show that while local thermal equilibrium holds in the
moving frame, relying on statistical methods such as distribution functions or
equipartition theorem are ultimately inconclusive in deciding on a correct
temperature transformation law (if any). | cond-mat_stat-mech |
Condensate density and superfluid mass density of a dilute Bose gas near
the condensation transition: We derive, through analysis of the structure of diagrammatic perturbation
theory, the scaling behavior of the condensate and superfluid mass density of a
dilute Bose gas just below the condensation transition. Sufficiently below the
critical temperature, $T_c$, the system is governed by the mean field
(Bogoliubov) description of the particle excitations. Close to $T_c$, however,
mean field breaks down and the system undergoes a second order phase
transition, rather than the first order transition predicted in Bogoliubov
theory. Both condensation and superfluidity occur at the same critical
temperature, $T_c$ and have similar scaling functions below $T_c$, but
different finite size scaling at $T_c$ to leading order in the system size.
Through a simple self-consistent two loop calculation we derive the critical
exponent for the condensate fraction, $2\beta\simeq 0.66$. | cond-mat_stat-mech |
Work distribution in thermal processes: We find the moment generating function (mgf) of the nonequilibrium work for
open systems undergoing a thermal process, ie, when the stochastic dynamics
maps thermal states into time dependent thermal states. The mgf is given in
terms of a temperature-like scalar satisfying a first order ODE. We apply the
result to some paradigmatic situations: a levitated nanoparticle in a breathing
optical trap, a brownian particle in a box with a moving piston and a two state
system driven by an external field, where the work mgfs are obtained for
different timescales and compared with Monte Carlo simulations. | cond-mat_stat-mech |
Machine-learning detection of the Berezinskii-Kosterlitz-Thouless
transition and the second-order phase transition in the XXZ models: We propose two machine-learning methods based on neural networks, which we
respectively call the phase-classification method and the
temperature-identification method, for detecting different types of phase
transitions in the XXZ models without prior knowledge of their critical
temperatures. The XXZ models have exchange couplings which are anisotropic in
the spin space where the strength is represented by a parameter $\Delta(>0)$.
The models exhibit the second-order phase transition when $\Delta>1$, whereas
the Berezinskii-Kosterlitz-Thouless (BKT) phase transition when $\Delta<1$. In
the phase-classification method, the neural network is trained using spin or
vortex configurations of well-known classical spin models other than the XXZ
models, e.g., the Ising models and the XY models, to classify those of the XXZ
models to corresponding phases. We demonstrate that the trained neural network
successfully detects the phase transitions for both $\Delta>1$ and $\Delta<1$,
and the evaluated critical temperatures coincide well with those evaluated by
conventional numerical calculations. In the temperature-identification method,
on the other hand, the neural network is trained so as to identify temperatures
at which the input spin or vortex configurations are generated by the Monte
Carlo thermalization. The critical temperatures are evaluated by analyzing the
optimized weight matrix, which coincide with the result of numerical
calculation for the second-order phase transition in the Ising-like XXZ model
with $\Delta=1.05$ but cannot be determined uniquely for the BKT transition in
the XY-like XXZ model with $\Delta=0.95$. | cond-mat_stat-mech |
Scaling behavior of a square-lattice Ising model with competing
interactions in a uniform field: Transfer-matrix methods, with the help of finite-size scaling and conformal
invariance concepts, are used to investigate the critical behavior of
two-dimensional square-lattice Ising spin-1/2 systems with first- and
second-neighbor interactions, both antiferromagnetic, in a uniform external
field. On the critical curve separating collinearly-ordered and paramagnetic
phases, our estimates of the conformal anomaly $c$ are very close to unity,
indicating the presence of continuously-varying exponents. This is confirmed by
direct calculations, which also lend support to a weak-universality picture;
however, small but consistent deviations from the Ising-like values $\eta=1/4$,
$\gamma/\nu=7/4$, $\beta/\nu=1/8$ are found. For higher fields, on the line
separating row-shifted $(2 \times 2)$ and disordered phases, we find values of
the exponent $\eta$ very close to zero. | cond-mat_stat-mech |
General Relation between Entanglement and Fluctuations in One Dimension: In one dimension very general results from conformal field theory and exact
calculations for certain quantum spin systems have established universal
scaling properties of the entanglement entropy between two parts of a critical
system. Using both analytical and numerical methods, we show that if particle
number or spin is conserved, fluctuations in a subsystem obey identical scaling
as a function of subsystem size, suggesting that fluctuations are a useful
quantity for determining the scaling of entanglement, especially in higher
dimensions. We investigate the effects of boundaries and subleading corrections
for critical spin and bosonic chains. | cond-mat_stat-mech |
Transition probabilities and dynamic structure factor in the ASEP
conditioned on strong flux: We consider the asymmetric simple exclusion processes (ASEP) on a ring
constrained to produce an atypically large flux, or an extreme activity. Using
quantum free fermion techniques we find the time-dependent conditional
transition probabilities and the exact dynamical structure factor under such
conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling
form. This gives a direct proof that the dynamical exponent in the extreme
current regime is $z=1$ rather than the KPZ exponent $z=3/2$ which
characterizes the ASEP in the regime of typical currents. Some of our results
extend to the activity in the partially asymmetric simple exclusion process,
including the symmetric case. | cond-mat_stat-mech |
Number Fluctuation and the Fundamental Theorem of Arithmetic: We consider N bosons occupying a discrete set of single-particle quantum
states in an isolated trap. Usually, for a given excitation energy, there are
many combinations of exciting different number of particles from the ground
state, resulting in a fluctuation of the ground state population. As a counter
example, we take the quantum spectrum to be logarithms of the prime number
sequence, and using the fundamental theorem of arithmetic, find that the ground
state fluctuation vanishes exactly for all excitations. The use of the standard
canonical or grand canonical ensembles, on the other hand, gives substantial
number fluctuation for the ground state. This difference between the
microcanonical and canonical results cannot be accounted for within the
framework of equilibrium statistical mechanics. | cond-mat_stat-mech |
On dissipation in crackling noise systems: We consider the amount of energy dissipated during individual avalanches at
the depinning transition of disordered and athermal elastic systems. Analytical
progress is possible in the case of the Alessandro-Beatrice-Bertotti-Montorsi
(ABBM) model for Barkhausen noise, due to an exact mapping between the energy
released in an avalanche and the area below a Brownian path until its first
zero-crossing. Scaling arguments and examination of an extended mean-field
model with internal structure show that dissipation relates to a critical
exponent recently found in a study of the rounding of the depinning transition
in presence of activated dynamics. A new numerical method to compute the
dynamic exponent at depinning in terms of blocked and marginally stable
configurations is proposed, and a kind of `dissipative anomaly'- with
potentially important consequences for nonequilibrium statistical mechanics- is
discussed. We conclude that for depinning systems the size of an avalanche does
not constitute by itself a univocal measure of the energy dissipated. | cond-mat_stat-mech |
Ergodicity breaking in one-dimensional reaction-diffusion systems: We investigate one-dimensional driven diffusive systems where particles may
also be created and annihilated in the bulk with sufficiently small rate. In an
open geometry, i.e., coupled to particle reservoirs at the two ends, these
systems can exhibit ergodicity breaking in the thermodynamic limit. The
triggering mechanism is the random motion of a shock in an effective potential.
Based on this physical picture we provide a simple condition for the existence
of a non-ergodic phase in the phase diagram of such systems. In the
thermodynamic limit this phase exhibits two or more stationary states. However,
for finite systems transitions between these states are possible. It is shown
that the mean lifetime of such a metastable state is exponentially large in
system-size. As an example the ASEP with the A0A--AAA reaction kinetics is
analyzed in detail. We present a detailed discussion of the phase diagram of
this particular model which indeed exhibits a phase with broken ergodicity. We
measure the lifetime of the metastable states with a Monte Carlo simulation in
order to confirm our analytical findings. | cond-mat_stat-mech |
Model simplification and loss of irreversibility: In this paper, we reveal a general relationship between model simplification
and irreversibility based on the model of continuous-time Markov chains with
time-scale separation. According to the topological structure of the fast
process, we divide the states of the chain into the transient states and the
recurrent states. We show that a two-time-scale chain can be simplified to a
reduced chain in two different ways: removal of the transient states and
aggregation of the recurrent states. Both the two operations will lead to a
decrease in the entropy production rate and its adiabatic part and will keep
its non-adiabatic part the same. This suggests that although model
simplification can retain almost all the dynamic information of the chain, it
will lose some thermodynamic information as a trade-off. | cond-mat_stat-mech |
A Fluctuation-Response Relation as a Probe of Long-Range Correlations in
Non-Equilibrium Quantum and Classical Fluids: The absence of a simple fluctuation-dissipation theorem is a major obstacle
for studying systems that are not in thermodynamic equilibrium. We show that
for a fluid in a non-equilibrium steady state characterized by a constant
temperature gradient the commutator correlation functions are still related to
response functions; however, the relation is to the bilinear response of
products of two observables, rather than to a single linear response function
as is the case in equilibrium. This modified fluctuation-response relation
holds for both quantum and classical systems. It is both motivated and informed
by the long-range correlations that exist in such a steady state and allows for
probing them via response experiments. This is of particular interest in
quantum fluids, where the direct observation of fluctuations by light
scattering would be difficult. In classical fluids it is known that the
coupling of the temperature gradient to the diffusive shear velocity leads to
correlations of various observables, in particular temperature fluctuations,
that do not decay as a function of distance, but rather extend over the entire
system. We investigate the nature of these correlations in a fermionic quantum
fluid and show that the crucial coupling between the temperature gradient and
velocity fluctuations is the same as in the classical case. Accordingly, the
nature of the long-ranged correlations in the hydrodynamic regime also is the
same. However, as one enters the collisionless regime in the low-temperature
limit the nature of the velocity fluctuations changes: they become ballistic
rather than diffusive. As a result, correlations of the temperature and other
observables are still singular in the long-wavelength limit, but the
singularity is weaker than in the hydrodynamic regime. | cond-mat_stat-mech |
Physical realization and possible identification of topological
excitations in quantum Heisenberg ferromagnet on lattice: Physical configurations corresponding to topological excitations present in
the XY limit of a quantum spin 1/2 Heisenberg ferromagnet, are investigated on
a two dimensional square lattice. Quantum vortices(anti-vortices) are
constructed in terms of terms of coherent spin field components and the crucial
role of the associated Wess-Zumino term is highlighted. It is shown that this
term can identify a large class of vortices(anti-vortices). In particular the
excitations with odd topological charge belonging to this class, are found to
exhibit a self-similar pattern regarding the internal charge distribution. Our
formalism is distinctly different from the coventional approach for the
construction of quantum vortices(anti-vortices). | cond-mat_stat-mech |
Emergence of extended Newtonian gravity from thermodynamics: Discovery of a novel thermodynamic aspect of nonrelativistic gravity is
reported. Here, initially, an unspecified scalar field potential is considered
and treated not as an externally applied field but as a thermodynamic variable
on an equal footing with the fluid variables. It is shown that the second law
of thermodynamics imposes a stringent constraint on the field, and, quite
remarkably, the allowable field turns out to be only of gravity. The resulting
field equation for the gravitational potential derived from the analysis of the
entropy production rate contains a dissipative term due to irreversibility. It
is found that the system relaxes to the conventional theory of Newtonian
gravity up to a certain spatial scale, whereas on the larger scale there
emerges non-Newtonian gravity described by a nonlinear field equation
containing a single coefficient. A comment is made on an estimation of the
coefficient that has its origin in the thermodynamic property of the system. | cond-mat_stat-mech |
Melting of Rare-Gas Crystals: Monte Carlo Simulation versus Experiments: We study the melting transition in crystals of rare gas Ar, Xe, and Kr by the
use of extensive Monte Carlo simulations with the Lennard-Jones potential. The
parameters of this potential have been deduced by Bernardes in 1958 from
experiments of rare gas in the gaseous phase. It is amazing that the parameters
of such a popular potential were not fully tested so far. In order to carry out
precise tests, we have written a high-performance Monte Carlo program which
allows in particular to take into account correctly the periodic boundary
conditions to reduce surface effects and to reduce CPU time. Using the
Bernardes parameters, we find that the melting temperature of several rare gas
is from 13 to 20% higher than that obtained from experiments. We have
throughout studied the case of Ar by examining both finite-size and
cutoff-distance effects. In order to get a good agreement with the experimental
melting temperature, we propose a modification of these parameters to describe
better the melting of rare-gas crystals. | cond-mat_stat-mech |
Thermodynamic Framework for Compact q-Gaussian Distributions: Recent works have associated systems of particles, characterized by
short-range repulsive interactions and evolving under overdamped motion, to a
nonlinear Fokker-Planck equation within the class of nonextensive statistical
mechanics, with a nonlinear diffusion contribution whose exponent is given by
$\nu=2-q$. The particular case $\nu=2$ applies to interacting vortices in
type-II superconductors, whereas $\nu>2$ covers systems of particles
characterized by short-range power-law interactions, where correlations among
particles are taken into account. In the former case, several studies presented
a consistent thermodynamic framework based on the definition of an effective
temperature $\theta$ (presenting experimental values much higher than typical
room temperatures $T$, so that thermal noise could be neglected), conjugated to
a generalized entropy $s_{\nu}$ (with $\nu=2$). Herein, the whole thermodynamic
scheme is revisited and extended to systems of particles interacting
repulsively, through short-ranged potentials, described by an entropy
$s_{\nu}$, with $\nu>1$, covering the $\nu=2$ (vortices in type-II
superconductors) and $\nu>2$ (short-range power-law interactions) physical
examples. The main results achieved are: (a) The definition of an effective
temperature $\theta$ conjugated to the entropy $s_{\nu}$; (b) The construction
of a Carnot cycle, whose efficiency is shown to be
$\eta=1-(\theta_2/\theta_1)$, where $\theta_1$ and $\theta_2$ are the effective
temperatures associated with two isothermal transformations, with
$\theta_1>\theta_2$; (c) Thermodynamic potentials, Maxwell relations, and
response functions. The present thermodynamic framework, for a system of
interacting particles under the above-mentioned conditions, and associated to
an entropy $s_{\nu}$, with $\nu>1$, certainly enlarges the possibility of
experimental verifications. | cond-mat_stat-mech |
Free energy calculations of a proton transfer reaction by simulated
tempering umbrella sampling first principles molecular dynamics simulations: A new simulated tempering method, which is referred to as simulated tempering
umbrella sampling, for calculating the free energy of chemical reactions is
proposed. First principles molecular dynamics simulations with this simulated
tempering were performed in order to study the intramolecular proton transfer
reaction of malonaldehyde in aqueous solution. Conformational sampling in
reaction coordinate space can be easily enhanced with this method, and the free
energy along a reaction coordinate can be calculated accurately. Moreover, the
simulated tempering umbrella sampling provides trajectory data more efficiently
than the conventional umbrella sampling method. | cond-mat_stat-mech |
Solution of the 2-star model of a network: The p-star model or exponential random graph is among the oldest and
best-known of network models. Here we give an analytic solution for the
particular case of the 2-star model, which is one of the most fundamental of
exponential random graphs. We derive expressions for a number of quantities of
interest in the model and show that the degenerate region of the parameter
space observed in computer simulations is a spontaneously symmetry broken phase
separated from the normal phase of the model by a conventional continuous phase
transition. | cond-mat_stat-mech |
Line Shape Broadening in Surface Diffusion of Interacting Adsorbates
with Quasielastic He Atom Scattering: The experimental line shape broadening observed in adsorbate diffusion on
metal surfaces with increasing coverage is usually related to the nature of the
adsorbate-adsorbate interaction. Here we show that this broadening can also be
understood in terms of a fully stochastic model just considering two noise
sources: (i) a Gaussian white noise accounting for the surface friction, and
(ii) a shot noise replacing the physical adsorbate-adsorbate interaction
potential. Furthermore, contrary to what could be expected, for relatively weak
adsorbate-substrate interactions the opposite effect is predicted: line shapes
get narrower with increasing coverage. | cond-mat_stat-mech |
What do generalized entropies look like? An axiomatic approach for
complex, non-ergodic systems: Shannon and Khinchin showed that assuming four information theoretic axioms
the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we
note that in physical systems one of these axioms may be violated. For
non-ergodic systems the so called separation axiom (Shannon-Khinchin axiom 4)
will in general not be valid. We show that when this axiom is violated the
entropy takes a more general form, $S_{c,d}\propto \sum_i ^W \Gamma(d+1, 1- c
\log p_i)$, where $c$ and $d$ are scaling exponents and $\Gamma(a,b)$ is the
incomplete gamma function. The exponents $(c,d)$ define equivalence classes for
all interacting and non interacting systems and unambiguously characterize any
statistical system in its thermodynamic limit. The proof is possible because of
two newly discovered scaling laws which any entropic form has to fulfill, if
the first three Shannon-Khinchin axioms hold. $(c,d)$ can be used to define
equivalence classes of statistical systems. A series of known entropies can be
classified in terms of these equivalence classes. We show that the
corresponding distribution functions are special forms of Lambert-${\cal W}$
exponentials containing -- as special cases -- Boltzmann, stretched exponential
and Tsallis distributions (power-laws). In the derivation we assume trace form
entropies, $S=\sum_i g(p_i)$, with $g$ some function, however more general
entropic forms can be classified along the same scaling analysis. | cond-mat_stat-mech |
Ground-state fidelity and tensor network states for quantum spin tubes: An efficient algorithm is developed for quantum spin tubes in the context of
the tensor network representations. It allows to efficiently compute the
ground-state fidelity per lattice site, which in turn enables us to identify
quantum critical points, at which quantum spin tubes undergo quantum phase
transitions. As an illustration, we investigate the isosceles spin 1/2
antiferromagnetic three-leg Heisenberg tube. Our simulation results suggest
that two Kosterlitz-Thouless transitions occur as the degree of asymmetry of
the rung interaction is tuned, thus offering an alternative route towards a
resolution to the conflicting results on this issue arising from the density
matrix renormalization group. | cond-mat_stat-mech |
Derivation of a statistical model for classical systems obeying
fractional exclusion principle: The violation of the Pauli principle has been surmised in several models of
the Fractional Exclusion Statistics and successfully applied to several quantum
systems. In this paper, a classical alternative of the exclusion statistics is
studied using the maximum entropy methods. The difference between the
Bose-Einstein statistics and the Maxwell-Boltzmann statistics is understood in
terms of a separable quantity, namely the degree of indistinguishability.
Starting from the usual Maxwell-Boltzmann microstate counting formula, a
special restriction related to the degree of indistinguishability is
incorporated using Lagrange multipliers to derive the probability distribution
function at equilibrium under NVE conditions. It is found that the resulting
probability distribution function generates real positive values within the
permissible range of parameters. For a dilute system, the probability
distribution function is intermediate between the Fermi-Dirac and Bose-Einstein
statistics and follows the exclusion principle. Properties of various variables
of this novel statistical model are studied and possible application to
classical thermodynamics is discussed. | cond-mat_stat-mech |
Long-term Relaxation of a Composite System in Partial Contact with a
Heat Bath: We study relaxational behavior from a highly excited state for a composite
system in partial contact with a heat bath, motivated by an experimental report
of long-term energy storage in protein molecules. The system consists of two
coupled elements: The first element is in direct contact with a heat bath,
while the second element interacts only with the first element. Due to this
indirect contact with the heat bath, energy injected into the second element
dissipates very slowly, according to a power law, whereas that injected into
the first one exhibits exponential dissipation. The relaxation equation
describing this dissipation is obtained analytically for both the underdamped
and overdamped limits. Numerical confirmation is given for both cases. | cond-mat_stat-mech |
Stretched-Gaussian asymptotics of the truncated Lévy flights for the
diffusion in nonhomogeneous media: The L\'evy, jumping process, defined in terms of the jumping size
distribution and the waiting time distribution, is considered. The jumping rate
depends on the process value. The fractional diffusion equation, which contains
the variable diffusion coefficient, is solved in the diffusion limit. That
solution resolves itself to the stretched Gaussian when the order parameter
$\mu\to2$. The truncation of the L\'evy flights, in the exponential and
power-law form, is introduced and the corresponding random walk process is
simulated by the Monte Carlo method. The stretched Gaussian tails are found in
both cases. The time which is needed to reach the limiting distribution
strongly depends on the jumping rate parameter. When the cutoff function falls
slowly, the tail of the distribution appears to be algebraic. | cond-mat_stat-mech |
Matrix Kesten Recursion, Inverse-Wishart Ensemble and Fermions in a
Morse Potential: The random variable $1+z_1+z_1z_2+\dots$ appears in many contexts and was
shown by Kesten to exhibit a heavy tail distribution. We consider natural
extensions of this variable and its associated recursion to $N \times N$
matrices either real symmetric $\beta=1$ or complex Hermitian $\beta=2$. In the
continuum limit of this recursion, we show that the matrix distribution
converges to the inverse-Wishart ensemble of random matrices. The full dynamics
is solved using a mapping to $N$ fermions in a Morse potential, which are
non-interacting for $\beta=2$. At finite $N$ the distribution of eigenvalues
exhibits heavy tails, generalizing Kesten's results in the scalar case. The
density of fermions in this potential is studied for large $N$, and the
power-law tail of the eigenvalue distribution is related to the properties of
the so-called determinantal Bessel process which describes the hard edge
universality of random matrices. For the discrete matrix recursion, using free
probability in the large $N$ limit, we obtain a self-consistent equation for
the stationary distribution. The relation of our results to recent works of
Rider and Valk\'o, Grabsch and Texier, as well as Ossipov, is discussed. | cond-mat_stat-mech |
The three faces of entropy for complex systems -- information,
thermodynamics and the maxent principle: There are three ways to conceptualize entropy: entropy as an extensive
thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs),
entropy as a measure for information production of ergodic sources (Shannon),
and entropy as a means for statistical inference on multinomial Bernoulli
processes (Jaynes maximum entropy principle). Even though these notions are
fundamentally different concepts, the functional form of the entropy for
thermodynamic systems in equilibrium, for ergodic sources in information
theory, and for independent sampling processes in statistical systems, is
degenerate, $H(p)=-\sum_i p_i\log p_i$. For many complex systems, which are
typically history-dependent, non-ergodic and non-multinomial, this is no longer
the case. Here we show that for such processes the three entropy concepts lead
to different functional forms of entropy. We explicitly compute these entropy
functionals for three concrete examples. For Polya urn processes, which are
simple self-reinforcing processes, the source information rate is $S_{\rm
IT}=\frac{1}{1-c}\frac1N \log N$, the thermodynamical (extensive) entropy is
$(c,d)$-entropy, $S_{\rm EXT}=S_{(c,0)}$, and the entropy in the maxent
principle (MEP) is $S_{\rm MEP}(p)=-\sum_i \log p_i$. For sample space reducing
(SSR) processes, which are simple path-dependent processes that are associated
with power law statistics, the information rate is $S_{\rm IT}=1+ \frac12 \log
W$, the extensive entropy is $S_{\rm EXT}=H(p)$, and the maxent result is
$S_{\rm MEP}(p)=H(p/p_1)+H(1-p/p_1)$. Finally, for multinomial mixture
processes, the information rate is given by the conditional entropy $\langle
H\rangle_f$, with respect to the mixing kernel $f$, the extensive entropy is
given by $H$, and the MEP functional corresponds one-to-one to the logarithm of
the mixing kernel. | cond-mat_stat-mech |
Note on the Kaplan-Yorke dimension and linear transport coefficients: A number of relations between the Kaplan-Yorke dimension, phase space
contraction, transport coefficients and the maximal Lyapunov exponents are
given for dissipative thermostatted systems, subject to a small external field
in a nonequilibrium stationary state. A condition for the extensivity of phase
space dimension reduction is given. A new expression for the transport
coefficients in terms of the Kaplan-Yorke dimension is derived. Alternatively,
the Kaplan-Yorke dimension for a dissipative macroscopic system can be
expressed in terms of the transport coefficients of the system. The agreement
with computer simulations for an atomic fluid at small shear rates is very
good. | cond-mat_stat-mech |
Defect Fluctuations and Lifetimes in Disordered Yukawa Systems: We examine the time dependent defect fluctuations and lifetimes for a
bidisperse disordered assembly of Yukawa particles. At high temperatures, the
noise spectrum of fluctuations is white and the coordination number lifetimes
have a stretched exponential distribution. At lower temperatures, the system
dynamically freezes, the defect fluctuations exhibit a 1/f spectrum, and there
is a power law distribution of the coordination number lifetimes. Our results
indicate that topological defect fluctuations may be a useful way to
characterize systems exhibiting dynamical heterogeneities. | cond-mat_stat-mech |
Many-body Green's function theory of Heisenberg films: The treatment of Heisenberg films with many-body Green's function theory
(GFT) is reviewed. The basic equations of GFT are derived in sufficient detail
so that the rest of the paper can be understood without having to consult
further literature. The main part of the paper is concerned with applications
of the formalism to ferromagnetic, antiferromagnetic and coupled
ferromagnetic-antiferromagnetic Heisenberg films based on a generalized
Tyablikov (RPA) decoupling of the exchange interaction and exchange anisotropy
terms and an Anderson-Callen decoupling for a weak single-ion anisotropy. We
not only give a consistent description of our own work but also refer
extensively to related investigations. We discuss in particular the
reorientation of the magnetization as a function of the temperature and film
thickness. If the single-ion anisotropy is strong, it can be treated exactly by
going to higher-order Green's functions. We also discuss the extension of the
theory beyond RPA. Finally the limitations of GFT is pointed out. | cond-mat_stat-mech |
Diatomic molecules in ultracold Fermi gases - Novel composite bosons: We give a brief overview of recent studies of weakly bound homonuclear
molecules in ultracold two-component Fermi gases. It is emphasized that they
represent novel composite bosons, which exhibit features of Fermi statistics at
short intermolecular distances. In particular, Pauli exclusion principle for
identical fermionic atoms provides a strong suppression of collisional
relaxation of such molecules into deep bound states. We then analyze
heteronuclear molecules which are expected to be formed in mixtures of
different fermionic atoms. It is found how an increase in the mass ratio for
the constituent atoms changes the physics of collisional stability of such
molecules compared to the case of homonuclear ones. We discuss Bose-Einstein
condensation of these composite bosons and draw prospects for future studies. | cond-mat_stat-mech |
Dynamical density-density correlations in the one-dimensional Bose gas: The zero-temperature dynamical structure factor of the one-dimensional Bose
gas with delta-function interaction (Lieb-Liniger model) is computed using a
hybrid theoretical/numerical method based on the exact Bethe Ansatz solution,
which allows to interpolate continuously between the weakly-coupled
Thomas-Fermi and strongly-coupled Tonks-Girardeau regimes. The results should
be experimentally accessible with Bragg spectroscopy. | cond-mat_stat-mech |
Scale Invariant Dynamics of Surface Growth: We describe in detail and extend a recently introduced nonperturbative
renormalization group (RG) method for surface growth. The scale invariant
dynamics which is the key ingredient of the calculation is obtained as the
fixed point of a RG transformation relating the representation of the
microscopic process at two different coarse-grained scales. We review the RG
calculation for systems in the Kardar-Parisi-Zhang universality class and
compute the roughness exponent for the strong coupling phase in dimensions from
1 to 9. Discussions of the approximations involved and possible improvements
are also presented. Moreover, very strong evidence of the absence of a finite
upper critical dimension for KPZ growth is presented. Finally, we apply the
method to the linear Edwards-Wilkinson dynamics where we reproduce the known
exact results, proving the ability of the method to capture qualitatively
different behaviors. | cond-mat_stat-mech |
Comment on "Tsallis power laws and finite baths with negative heat
capacity" [Phys. Rev. E 88, 042126 (2013)]: In [Phys. Rev. E 88, 042126 (2013)] it is stated that Tsallis distributions
do not emerge from thermalization with a "bath" of finite, energy-independent,
heat capacity. We report evidence for the contrary. | cond-mat_stat-mech |
How many eigenvalues of a Gaussian random matrix are positive?: We study the probability distribution of the index ${\mathcal N}_+$, i.e.,
the number of positive eigenvalues of an $N\times N$ Gaussian random matrix. We
show analytically that, for large $N$ and large $\mathcal{N}_+$ with the
fraction $0\le c=\mathcal{N}_+/N\le 1$ of positive eigenvalues fixed, the index
distribution $\mathcal{P}({\mathcal N}_+=cN,N)\sim\exp[-\beta N^2 \Phi(c)]$
where $\beta$ is the Dyson index characterizing the Gaussian ensemble. The
associated large deviation rate function $\Phi(c)$ is computed explicitly for
all $0\leq c \leq 1$. It is independent of $\beta$ and displays a quadratic
form modulated by a logarithmic singularity around $c=1/2$. As a consequence,
the distribution of the index has a Gaussian form near the peak, but with a
variance $\Delta(N)$ of index fluctuations growing as $\Delta(N)\sim \log
N/\beta\pi^2$ for large $N$. For $\beta=2$, this result is independently
confirmed against an exact finite $N$ formula, yielding $\Delta(N)= \log
N/2\pi^2 +C+\mathcal{O}(N^{-1})$ for large $N$, where the constant $C$ has the
nontrivial value $C=(\gamma+1+3\log 2)/2\pi^2\simeq 0.185248...$ and
$\gamma=0.5772...$ is the Euler constant. We also determine for large $N$ the
probability that the interval $[\zeta_1,\zeta_2]$ is free of eigenvalues. Part
of these results have been announced in a recent letter [\textit{Phys. Rev.
Lett.} {\bf 103}, 220603 (2009)]. | cond-mat_stat-mech |
Random walks and Brownian motion: A method of computation for
first-passage times and related quantities in confined geometries: In this paper we present a computation of the mean first-passage times both
for a random walk in a discrete bounded lattice, between a starting site and a
target site, and for a Brownian motion in a bounded domain, where the target is
a sphere. In both cases, we also discuss the case of two targets, including
splitting probabilities, and conditional mean first-passage times. In addition,
we study the higher-order moments and the full distribution of the
first-passage time. These results significantly extend our earlier contribution
[Phys. Rev. Lett. 95, 260601]. | cond-mat_stat-mech |
The expression of ensemble average internal energy in long-range
interaction complex system and its statistical physical properties: In this paper, we attempt to derive the expression of ensemble average
internal energy in long-range interaction complex system. Further, the Shannon
entropy hypothesis is used to derive the probability distribution function of
energy. It is worth mentioning that the probability distribution function of
energy can be equivalent to the q-Gaussian distribution given by Tsallis based
on nonextensive entropy. In order to verify the practical significance of this
model, it is applied to the older subject of income system. The classic income
distribution is two-stage, the most recognized low-income distribution is the
exponential form, and the high-income distribution is the recognized Pareto
power law distribution. The probability distribution can explain the entire
distribution of United States income data. In addition, the internal energy,
entropy and temperature of the United States income system can be calculated,
and the economic crisis in the United States in recent years can be presented.
It is believed that the model will be further improved and extended to other
areas. | cond-mat_stat-mech |
Assessment of kinetic theories for moderately dense granular binary
mixtures: Shear viscosity coefficient: Two different kinetic theories [J. Solsvik and E. Manger (SM-theory), Phys.
Fluids \textbf{33}, 043321 (2021) and V. Garz\'o, J. W. Dufty, and C. M. Hrenya
(GDH-theory), Phys. Rev. E \textbf{76}, 031303 (2007)] are considered to
determine the shear viscosity $\eta$ for a moderately dense granular binary
mixture of smooth hard spheres. The mixture is subjected to a simple shear flow
and heated by the action of an external driving force (Gaussian thermostat)
that exactly compensates the energy dissipated in collisions. The set of Enskog
kinetic equations is the starting point to obtain the dependence of $\eta$ on
the control parameters of the mixture: solid fraction, concentration, mass and
diameter ratios, and coefficients of normal restitution. While the expression
of $\eta$ found in the SM-theory is based on the assumption of Maxwellian
distributions for the velocity distribution functions of each species, the
GDH-theory solves the Enskog equation by means of the Chapman--Enskog method to
first order in the shear rate. To assess the accuracy of both kinetic theories,
the Enskog equation is numerically solved by means of the direct simulation
Monte Carlo (DSMC) method. The simulation is carried out for a mixture under
simple shear flow, using the thermostat to control the cooling effects. Given
that the SM-theory predicts a vanishing kinetic contribution to the shear
viscosity, the comparison between theory and simulations is essentially made at
the level of the collisional contribution $\eta_c$ to the shear viscosity. The
results clearly show that the GDH-theory compares with simulations much better
than the SM-theory over a wide range of values of the coefficients of
restitution, the volume fraction, and the parameters of the mixture (masses,
diameters, and concentration). | cond-mat_stat-mech |
Hierarchical Organization in Complex Networks: Many real networks in nature and society share two generic properties: they
are scale-free and they display a high degree of clustering. We show that these
two features are the consequence of a hierarchical organization, implying that
small groups of nodes organize in a hierarchical manner into increasingly large
groups, while maintaining a scale-free topology. In hierarchical networks the
degree of clustering characterizing the different groups follows a strict
scaling law, which can be used to identify the presence of a hierarchical
organization in real networks. We find that several real networks, such as the
World Wide Web, actor network, the Internet at the domain level and the
semantic web obey this scaling law, indicating that hierarchy is a fundamental
characteristic of many complex systems. | cond-mat_stat-mech |
On the maximum entropy principle and the minimization of the Fisher
information in Tsallis statistics: We give a new proof of the theorems on the maximum entropy principle in
Tsallis statistics. That is, we show that the $q$-canonical distribution
attains the maximum value of the Tsallis entropy, subject to the constraint on
the $q$-expectation value and the $q$-Gaussian distribution attains the maximum
value of the Tsallis entropy, subject to the constraint on the $q$-variance, as
applications of the nonnegativity of the Tsallis relative entropy, without
using the Lagrange multipliers method. In addition, we define a $q$-Fisher
information and then prove a $q$-Cram\'er-Rao inequality that the $q$-Gaussian
distribution with special $q$-variances attains the minimum value of the
$q$-Fisher information. | cond-mat_stat-mech |
Dynamical Properties of the Slithering Snake Algorithm: A numerical test
of the activated reptation hypothesis: The correlations in the motion of reptating polymers in their melt are
investigated by means of kinetic Monte Carlo simulations of the three
dimensional slithering snake version of the bond-fluctuation model.
Surprisingly, the slithering snake dynamics becomes inconsistent with
classical reptation predictions at high chain overlap (either chain length $N$
or volume fraction $\phi$) where the relaxation times increase much faster than
expected.
This is due to the anomalous curvilinear diffusion in a finite time window
whose upper bound $\tau_+$ is set by the chain end density $\phi/N$. Density
fluctuations created by passing chain ends allow a reference polymer to break
out of the local cage of immobile obstacles created by neighboring chains.
The dynamics of dense solutions of snakes at $t \ll \tau_+$ is identical to
that of a benchmark system where all but one chain are frozen. We demonstrate
that it is the slow creeping of a chain out of its correlation hole which
causes the subdiffusive dynamical regime.
Our results are in good qualitative agreement with the activated reptation
scheme proposed recently by Semenov and Rubinstein [Eur. Phys. J. B, {\bf 1}
(1998) 87].
Additionally, we briefly comment on the relevance of local relaxation
pathways within a slithering snake scheme. Our preliminary results suggest that
a judicious choice of the ratio of local to slithering snake moves is crucial
to equilibrate a melt of long chains efficiently. | cond-mat_stat-mech |
Effect of Strong Magnetic Fields on the Equilibrium of a Degenerate Gas
of Nucleons and Electrons: We obtain the equations that define the equilibrium of a homogeneous
relativistic gas of neutrons, protons and electrons in a constant magnetic
field as applied to the conditions that probably occur near the center of
neutron stars. We compute the relative densities of the particles at
equilibrium and the Fermi momentum of electrons in the strong magnetic field as
function of the density of neutrons and the magnetic field induction. Novel
features are revealed as to the ratio of the number of protons to the number of
neutrons at equilibrium in the presence of large magnetic fields. | cond-mat_stat-mech |
A recipe for an unpredictable random number generator: In this work we present a model for computation of random processes in
digital computers which solves the problem of periodic sequences and hidden
errors produced by correlations. We show that systems with non-invertible
non-linearities can produce unpredictable sequences of independent random
numbers. We illustrate our result with some numerical calculations related with
random walks simulations. | cond-mat_stat-mech |
Entanglement, combinatorics and finite-size effects in spin-chains: We carry out a systematic study of the exact block entanglement in XXZ
spin-chain at Delta=-1/2. We present, the first analytic expressions for
reduced density matrices of n spins in a chain of length L (for n<=6 and
arbitrary but odd L) of a truly interacting model. The entanglement entropy,
the moments of the reduced density matrix, and its spectrum are then easily
derived. We explicitely construct the "entanglement Hamiltonian" as the
logarithm of this matrix. Exploiting the degeneracy of the ground-state, we
find the scaling behavior of entanglement of the zero-temperature mixed state. | cond-mat_stat-mech |
Homogeneous bubble nucleation in water at negative pressure: A Voronoi
polyhedra analysis: We investigate vapor bubble nucleation in metastable TIP4P/2005 water at
negative pressure via the Mean First Passage Time (MFPT) method using the
volume of the largest bubble as a local order parameter. We identify the
bubbles in the system by means of a Voronoi-based analysis of the Molecular
Dynamics trajectories. By comparing the features of the tessellation of liquid
water at ambient conditions to those of the same system with an empty cavity we
are able to discriminate vapor (or interfacial) molecules from the bulk ones.
This information is used to follow the time evolution of the largest bubble
until the system cavitates at 280 K above and below the spinodal line. At the
pressure above the spinodal line, the MFPT curve shows the expected shape for a
moderately metastable liquid from which we estimate the bubble nucleation rate
and the size of the critical cluster. The nucleation rate estimated using
Classical Nucleation Theory turns out to be about 8 order of magnitude lower
than the one we compute by means of MFPT. The behavior at the pressure below
the spinodal line, where the liquid is thermodynamically unstable, is
remarkably different, the MFPT curve being a monotonous function without any
inflection point. | cond-mat_stat-mech |
Dynamic asset trees and Black Monday: The minimum spanning tree, based on the concept of ultrametricity, is
constructed from the correlation matrix of stock returns. The dynamics of this
asset tree can be characterised by its normalised length and the mean
occupation layer, as measured from an appropriately chosen centre called the
`central node'. We show how the tree length shrinks during a stock market
crisis, Black Monday in this case, and how a strong reconfiguration takes
place, resulting in topological shrinking of the tree. | cond-mat_stat-mech |
Disordered systems and Burgers' turbulence: Talk presented at the International Conference on Mathematical Physics
(Brisbane 1997). This is an introduction to recent work on the scaling and
intermittency in forced Burgers turbulence. The mapping between Burgers'
equation and the problem of a directed polymer in a random medium is used in
order to study the fully developped turbulence in the limit of large
dimensions. The stirring force corresponds to a quenched (spatio temporal)
random potential for the polymer, correlated on large distances. A replica
symmetry breaking solution of the polymer problem provides the full probability
distribution of the velocity difference $u(r)$ between points separated by a
distance $r$ much smaller than the correlation length of the forcing. This
exhibits a very strong intermittency which is related to regions of shock
waves, in the fluid, and to the existence of metastable states in the directed
polymer problem. We also mention some recent computations on the finite
dimensional problem, based on various analytical approaches (instantons,
operator product expansion, mapping to directed polymers), as well as a
conjecture on the relevance of Burgers equation (with the length scale playing
the role of time) for the description of the functional renormalisation group
flow for the effective pinning potential of a manifold pinned by impurities. | cond-mat_stat-mech |
Dynamical transition in the TASEP with Langmuir kinetics: mean-field
theory: We develop a mean-field theory for the totally asymmetric simple exclusion
process (TASEP) with open boundaries, in order to investigate the so-called
dynamical transition. The latter phenomenon appears as a singularity in the
relaxation rate of the system toward its non-equilibrium steady state. In the
high-density (low-density) phase, the relaxation rate becomes independent of
the injection (extraction) rate, at a certain critical value of the parameter
itself, and this transition is not accompanied by any qualitative change in the
steady-state behavior. We characterize the relaxation rate by providing
rigorous bounds, which become tight in the thermodynamic limit. These results
are generalized to the TASEP with Langmuir kinetics, where particles can also
bind to empty sites or unbind from occupied ones, in the symmetric case of
equal binding/unbinding rates. The theory predicts a dynamical transition to
occur in this case as well. | cond-mat_stat-mech |
Driven tracers in narrow channels: Steady state properties of a driven tracer moving in a narrow two dimensional
(2D) channel of quiescent medium are studied. The tracer drives the system out
of equilibrium, perturbs the density and pressure fields, and gives the bath
particles a nonzero average velocity, creating a current in the channel. Three
models in which the confining effect of the channel is probed are analyzed and
compared in this study: the first is the simple symmetric exclusion process
(SSEP), for which the stationary density profile and the pressure on the walls
in the frame of the tracer are computed. We show that the tracer acts like a
dipolar source in an average velocity field. The spatial structure of this 2D
strip is then simplified to a one dimensional SSEP, in which exchanges of
position between the tracer and the bath particles are allowed. Using a
combination of mean field theory and exact solution in the limit where no
exchange is allowed, gives good predictions of the velocity of the tracer and
the density field. Finally, we show that results obtained for the 1D SSEP with
exchanges also apply to a gas of overdamped hard disks in a narrow channel. The
correspondence between the parameters of the SSEP and of the gas of hard disks
is systematic and follows from simple intuitive arguments. Our analytical
results are checked numerically. | cond-mat_stat-mech |
Predictive statistical mechanics and macroscopic time evolution. A model
for closed Hamiltonian systems: Predictive statistical mechanics is a form of inference from available data,
without additional assumptions, for predicting reproducible phenomena. By
applying it to systems with Hamiltonian dynamics, a problem of predicting the
macroscopic time evolution of the system in the case of incomplete information
about the microscopic dynamics was considered. In the model of a closed
Hamiltonian system (i.e. system that can exchange energy but not particles with
the environment) that with the Liouville equation uses the concepts of
information theory, analysis was conducted of the loss of correlation between
the initial phase space paths and final microstates, and the related loss of
information about the state of the system. It is demonstrated that applying the
principle of maximum information entropy by maximizing the conditional
information entropy, subject to the constraint given by the Liouville equation
averaged over the phase space, leads to a definition of the rate of change of
entropy without any additional assumptions. In the subsequent paper
(http://arxiv.org/abs/1506.02625) this basic model is generalized further and
brought into direct connection with the results of nonequilibrium theory. | cond-mat_stat-mech |
Kibble-Zurek mechanism and infinitely slow annealing through critical
points: We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase
ordering systems during an infinitely slow annealing across a second order
phase transition. We elucidate the time and cooling rate dependence of the
typical growing length and we use it to predict the number of topological
defects left over in the symmetry broken phase as a function of time, both
close and far from the critical region. Our results extend the Kibble-Zurek
mechanism and reveal its limitations. | cond-mat_stat-mech |
Equilibrium Equality for Free Energy Difference: Jarzynski Equality (JE) and the thermodynamic integration method are
conventional methods to calculate free energy difference (FED) between two
equilibrium states with constant temperature of a system. However, a number of
ensemble samples should be generated to reach high accuracy for a system with
large size, which consumes a lot computational resource. Previous work had
tried to replace the non-equilibrium quantities with equilibrium quantities in
JE by introducing a virtual integrable system and it had promoted the
efficiency in calculating FED between different equilibrium states with
constant temperature. To overcome the downside that the FED for two equilibrium
states with different temperature can't be calculated efficiently in previous
work, this article derives out the Equilibrium Equality for FED between any two
different equilibrium states by deriving out the equality for FED between
states with different temperatures and then combining the equality for FED
between states with different volumes. The equality presented in this article
expresses FED between any two equilibrium states as an ensemble average in one
equilibrium state, which enable the FED between any two equilibrium states can
be determined by generating only one canonical ensemble and thus the samples
needed are dramatically less and the efficiency is promoted a lot. Plus, the
effectiveness and efficiency of the equality are examined in Toda-Lattice model
with different dimensions. | cond-mat_stat-mech |
Relaxation and coarsening of weakly-interacting breathers in a
simplified DNLS chain: The Discrete NonLinear Schr\"odinger (DNLS) equation displays a parameter
region characterized by the presence of localized excitations (breathers).
While their formation is well understood and it is expected that the asymptotic
configuration comprises a single breather on top of a background, it is not
clear why the dynamics of a multi-breather configuration is essentially frozen.
In order to investigate this question, we introduce simple stochastic models,
characterized by suitable conservation laws. We focus on the role of the
coupling strength between localized excitations and background. In the DNLS
model, higher breathers interact more weakly, as a result of their faster
rotation. In our stochastic models, the strength of the coupling is controlled
directly by an amplitude-dependent parameter. In the case of a power-law
decrease, the associated coarsening process undergoes a slowing down if the
decay rate is larger than a critical value. In the case of an exponential
decrease, a freezing effect is observed that is reminiscent of the scenario
observed in the DNLS. This last regime arises spontaneously when direct energy
diffusion between breathers and background is blocked below a certain
threshold. | cond-mat_stat-mech |
Quantum Annealing - Foundations and Frontiers: We briefly review various computational methods for the solution of
optimization problems. First, several classical methods such as Metropolis
algorithm and simulated annealing are discussed. We continue with a description
of quantum methods, namely adiabatic quantum computation and quantum annealing.
Next, the new D-Wave computer and the recent progress in the field claimed by
the D-Wave group are discussed. We present a set of criteria which could help
in testing the quantum features of these computers. We conclude with a list of
considerations with regard to future research. | cond-mat_stat-mech |
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