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The Feynman effective classical potential in the Schrödinger
formulation: New physical insight into the correspondence between path integral concepts
and the Schr\"odinger formulation is gained by the analysis of the effective
classical potential, that is defined within the Feynman path integral
formulation of statistical mechanics. This potential is related to the
quasi-static response of the equilibrium system to an external force. These
findings allow for a comprehensive formulation of dynamical approximations
based on this potential. | cond-mat_stat-mech |
Quantum phase transitions of the extended isotropic XY model with
long-range interactions: The one-dimensional extended isotropic XY model (s=1/2) in a transverse field
with uniform long-range interactions among the \textit{z} components of the
spin is considered. The model is exactly solved by introducing the gaussian and
Jordan-Wigner transformations, which map it in a non-interacting fermion
system. The partition function can be determined in closed form at arbitrary
temperature and for arbitrary multiplicity of the multiple spin interaction.
From this result all relevant thermodynamic functions are obtained and, due
to the long-range interactions, the model can present classical and quantum
transitions of first- and second-order. The study of its critical behavior is
restricted for the quantum transitions, which are induced by the transverse
field at $T=0.$ The phase diagram is explicitly obtained for multiplicities
$p=2,3,4$ and $\infty ,$ as a function of the interaction parameters, and, in
these cases, the critical behavior of the model is studied\textbf{\}in detail.
Explicit results are also presented for the induced magnetization and
isothermal susceptibility $\chi_{T}^{zz}$, and a detailed analysis is also
carried out for the static longitudinal $<S_{j}^{z}S_{l}^{z}>$ and transversal
$<S_{j}^{x}S_{l}^{x}>$ correlation functions. The different phases presented by
the model can be characterized by the spatial decay of the these correlations,
and from these results some of these can be classified as quantum spin liquid
phases. The static critical exponents and the dynamic one, $z,$ have also been
determined, and it is shown that, besides inducing first order phase
transition, the long-range interaction also changes the universality class the
model.-range interaction also changes the universality class the model. | cond-mat_stat-mech |
Many-particle dephasing after a quench: After a quench in a quantum many-body system, expectation values tend to
relax towards long-time averages. However, in any finite-size system, temporal
fluctuations remain. It is crucial to study the suppression of these
fluctuations with system size. The particularly important case of
non-integrable models has been addressed so far only by numerics and
conjectures based on analytical bounds. In this work, we are able to derive
analytical predictions for the temporal fluctuations in a non-integrable model
(the transverse Ising chain with extra terms). Our results are based on
identifying a dynamical regime of 'many-particle dephasing', where
quasiparticles do not yet relax but fluctuations are nonetheless suppressed
exponentially by weak integrability breaking. | cond-mat_stat-mech |
Essentially Ergodic Behaviour: I prove a theorem on the precise connection of the time and phase space
average of the Boltzmann equilibrium showing that the behaviour of a dynamical
system with a stationary measure and a dominant equilibrium state is
qualitatively ergodic. | cond-mat_stat-mech |
Accuracy of energy measurement and reversible operation of a
microcanonical Szilard engine: In a recent paper [Vaikuntanathan and Jarzynski, Phys. Rev. E {\bf 83},
061120 (2011), arXiv:1105.1744] a model was introduced whereby work could be
extracted from a thermal bath by measuring the energy of a particle that was
thermalized by the bath and manipulating the potential of the particle in the
appropriate way, depending on the measurement outcome. If the extracted work is
$W_1$ and the work $W_{\text{er}}$ needed to be dissipated in order to erase
the measured information in accordance with Landauer's principle, it was shown
that $W_1\leq W_{\text{er}}$ in accordance with the second law of
thermodynamics. Here we extend this work in two directions: First, we discuss
how accurately the energy should be measured. By increasing the accuracy one
can extract more work, but at the same time one obtains more information that
has to be deleted. We discuss what are the appropriate ways of optimizing the
balance between the two and find optimal solutions. Second, whenever $W_1$ is
strictly less than $W_{\text{er}}$ it means that an irreversible step has been
performed. We identify the irreversible step and propose a protocol that will
achieve the same transition in a reversible way, increasing $W_1$ so that $W_1
= W_{\text{er}}$. | cond-mat_stat-mech |
Non mean-field behaviour of critical wetting transition for short-range
forces: Critical wetting transition for short-range forces in three dimensions
($d=3$) is reinvestigated by means of Monte Carlo simulation. Using anisotropic
finite size scaling approach, as well as approaches that do not rely on finite
size scaling, we show that the critical wetting transition shows clear
deviation from mean-field behaviour. We estimate that the effective critical
exponent $\nu_{\|}^{\textrm{eff}}=1.76\pm 0.08$ for $J/kT=0.35$ and
$\nu_{\|}^{\textrm{eff}}=1.85\pm 0.07$ for $J/kT=0.25$. These values are in
accord with predictions of Parry {\it et al.} [Phys. Rev. Lett. {\bf 100},
136105 (2008)]. We also point out that the anisotropic finite size scaling
approach in $d=3$ requires additional modification in order to reach full
consistency of simulational results. | cond-mat_stat-mech |
Dynamic Mean-Field Glass Model with Reversible Mode Coupling and Trivial
Hamiltonian: Often the current mode coupling theory (MCT) of glass transitions is compared
with mean field theories. We explore this possible correspondence. After
showing a simple-minded derivation of MCT with some difficulties we give a
concise account of our toy model developed to gain more insight into MCT. We
then reduce this toy model by adiabatically eliminating rapidly varying
velocity-like variables to obtain a Fokker-Planck equation for the slowly
varying density-like variables where diffusion matrix can be singular. This
gives a room for nonergodic stationary solutions of the above equation. | cond-mat_stat-mech |
Separation of spin and charge in the continuum Schrödinger equation: I describe here the attempt to introduce spin-charge separation in
Schrodinger equation. The construction we present here gives a decomposed
Schrodinger spinor that has one problem: Its absolute value can only have value
between 0 and ${1}{2}$. The problem we solve is to expand and generalize this
construction so that one can have a Schrodinger spinor with absolute value that
are arbitrary non-negative numbers. It may be that one has to introduce a set
of different decompositions to cover all nonnegative values, that is to
introduce patches over $\mathbb{R}_{+}^{3}$ so that in each patch one has a
different representation. It seems that the decomposition has a direct relation
to so called entangled states that have been discussed very much in connection
of e.g. quantum computing, and we would like to find this relation and discuss
it in detail. | cond-mat_stat-mech |
Scaling laws for diffusion on (trans)fractal scale-free networks: Fractal (or transfractal) features are common in real-life networks and are
known to influence the dynamic processes taking place in the network itself.
Here we consider a class of scale-free deterministic networks, called
$(u,v)$-flowers, whose topological properties can be controlled by tuning the
parameters $u$ and $v$; in particular, for $u>1$, they are fractals endowed
with a fractal dimension $d_f$, while for $u=1$, they are transfractal endowed
with a transfractal dimension $\tilde{d}_f$. In this work we investigate
dynamic processes (i.e., random walks) and topological properties (i.e., the
Laplacian spectrum) and we show that, under proper conditions, the same
scalings (ruled by the related dimensions), emerge for both fractal and
transfractal. | cond-mat_stat-mech |
Thermodynamic relations at the coupling boundary in adaptive resolution
simulations for open systems: The adaptive resolution simulation (AdResS) technique couples regions with
different molecular resolutions and allows the exchange of molecules between
different regions in an adaptive fashion. The latest development of the
technique allows to abruptly couple the atomistically resolved region with a
region of non-interacting point-like particles. The abrupt set-up was derived
having in mind the idea of the atomistically resolved region as an open system
embedded in a large reservoir at a given macroscopic state. In this work,
starting from the idea of open system, we derive thermodynamic relations for
AdResS which justify conceptually and numerically the claim of AdResS as a
technique for simulating open systems. In particular, we derive the relation
between the chemical potential of the AdResS set-up and that of its reference
fully atomistic simulation. The implication of this result is that the grand
potential of AdResS can be explicitly written and thus, from a statistical
mechanics point of view, the atomistically resolved region of AdResS can be
identified with a well defined open system. | cond-mat_stat-mech |
Optimal inference strategies and their implications for the linear noise
approximation: We study the information loss of a class of inference strategies that is
solely based on time averaging. For an array of independent binary sensors
(e.g., receptors, single electron transistors) measuring a weak random signal
(e.g., ligand concentration, gate voltage) this information loss is up to 0.5
bit per measurement irrespective of the number of sensors. We derive a
condition related to the local detailed balance relation that determines
whether or not such a loss of information occurs. Specifically, if the free
energy difference arising from the signal is symmetrically distributed among
the forward and backward rates, time integration mechanisms will capture the
full information about the signal. As an implication, for the linear noise
approximation, we can identify the same loss of information, arising from its
inherent simplification of the dynamics. | cond-mat_stat-mech |
Special flow model for passive particle transport considering internal
noise: We have generalized the semi-analytic approach of special flow to the
description of flows of passive particles taking into account internal noise.
The model is represented by a series of recurrence relations. The recurrence
relations are constructed by numerically solving the Langevin equations in the
presence of a random force, for an ensemble of passive particles during
transport through a secluded cell. This approach allows us to estimate the
transit time dependence near stagnation points for fluid elements carried by
the flow. Such estimates are obtained for the most important types of
stagnation points. It is shown that macroscopic transport of an ensemble of
particles through such a lattice is possible only when internal noise is taken
into account. For Gaussian and non-Gaussian noise at low intensity the transit
time has one peak, which is a consequence of the existence of vortices of one
stagnation point. Increase of noise intensity leads to slowing down of particle
transport. | cond-mat_stat-mech |
Finite-size scaling as a way to probe near-criticality in natural swarms: Collective behaviour in biological systems is often accompanied by strong
correlations. The question has therefore arisen of whether correlation is
amplified by the vicinity to some critical point in the parameters space.
Biological systems, though, are typically quite far from the thermodynamic
limit, so that the value of the control parameter at which correlation and
susceptibility peak depend on size. Hence, a system would need to readjust its
control parameter according to its size in order to be maximally correlated.
This readjustment, though, has never been observed experimentally. By gathering
three-dimensional data on swarms of midges in the field we find that swarms
tune their control parameter and size so as to maintain a scaling behaviour of
the correlation function. As a consequence, correlation length and
susceptibility scale with the system's size and swarms exhibit a near-maximal
degree of correlation at all sizes. | cond-mat_stat-mech |
A Numerical Study on the Evolution of Portfolio Rules: Is CAPM Fit for
Nasdaq?: In this paper we test computationally the performance of CAPM in an
evolutionary setting. In particular we study the stability of wealth
distribution in a financial market where some traders invest as prescribed by
CAPM and others behave according to different portfolio rules. Our study is
motivated by recent analytical results that show that, whenever a logarithmic
utility maximiser enters the market, traders who either ``believe'' in CAPM and
use it as a rule of thumb for their portfolio decisions, or are endowed with
genuine mean-variance preferences, vanish in the long run. Our analysis
provides further insights and extends these results. We simulate a sequence of
trades in a financial market and: first, we address the issue of how long is
the long run in different parametric settings; second, we study the effect of
heterogeneous savings behaviour on asymptotic wealth shares. We find that CAPM
is particularly ``unfit'' for highly risky environments. | cond-mat_stat-mech |
Anomalous cooling and heating - the Mpemba effect and its inverse: Under certain conditions, it takes a shorter time to cool a hot system than
to cool the same system initiated at a lower temperature. This phenomenon - the
"Mpemba Effect" - is well known in water, and has recently been observed in
other systems as well. However, there is no single generic mechanism that
explains this counter-intuitive behavior. Using the theoretical framework of
non-equilibrium thermodynamics, we present a widely applicable mechanism for
this effect, derive a sufficient condition for its appearance in Markovian
dynamics, and predict an inverse Mpemba effect in heating: under proper
conditions, a cold system can heat up faster than the same system initiated at
a higher temperature. Our results suggest that it should be possible to observe
the Mpemba effect and its inverse in a variety of systems, where they have
never been demonstrated before. | cond-mat_stat-mech |
On the microscopic foundation of thermodynamics and kinetics. Current
status and prospects: A comparative analysis of two concepts aimed at microscopic substantiation of
thermodynamics and kinetics has been performed. The first concept is based on
the idea of microscopic reversibility of the dynamics of a system of particles,
while macroscopic irreversibility is of statistical origin. The second concept
is based on the idea of the initial microscopic irreversibility of dynamics,
one of the mechanisms of which is the relativistic retardation of interactions
between particles. | cond-mat_stat-mech |
Spectral properties of three-dimensional Anderson model: The three-dimensional Anderson model represents a paradigmatic model to
understand the Anderson localization transition. In this work we first review
some key results obtained for this model in the past 50 years, and then study
its properties from the perspective of modern numerical approaches. Our main
focus is on the quantitative comparison between the level sensitivity
statistics and the level statistics. While the former studies the sensitivity
of Hamiltonian eigenlevels upon inserting a magnetic flux, the latter studies
the properties of unperturbed eigenlevels. We define two versions of
dimensionless conductance, the first corresponding to the width of the level
curvature distribution relative to the mean level spacing, and the second
corresponding to the ratio of the Heisenberg and the Thouless time obtained
from the spectral form factor. We show that both conductances look remarkably
similar around the localization transition, in particular, they predict a
nearly identical critical point consistent with other measures of the
transition. We then study some further properties of those quantities: for
level curvatures, we discuss particular similarities and differences between
the width of the level curvature distribution and the characteristic energy
studied by Edwards and Thouless in their pioneering work [J. Phys. C. 5, 807
(1972)]. In the context of the spectral form factor, we show that at the
critical point it enters a broad time-independent regime, in which its value is
consistent with the level compressibility obtained from the level variance.
Finally, we test the scaling solution of the average level spacing ratio in the
crossover regime using the cost function minimization approach introduced in
[Phys. Rev. B. 102, 064207 (2020)]. We find that the extracted transition point
and the scaling coefficient agree with those from the literature to high
numerical accuracy. | cond-mat_stat-mech |
Dichotomous acceleration process in one dimension: Position fluctuations: We study the motion of a one-dimensional particle which reverses its
direction of acceleration stochastically. We focus on two contrasting
scenarios, where the waiting-times between two consecutive acceleration
reversals are drawn from (i) an exponential distribution and (ii) a power-law
distribution $\rho(\tau)\sim \tau^{-(1+\alpha)}$. We compute the mean, variance
and short-time distribution of the position $x(t)$ using a trajectory-based
approach. We show that, while for the exponential waiting-time, $\langle
x^2(t)\rangle\sim t^3$ at long times, for the power-law case, a non-trivial
algebraic growth $\langle x^2(t)\rangle \sim t^{2\phi(\alpha)}$ emerges, where
$\phi(\alpha)=2$, $(5-\alpha)/2,$ and $3/2$ for $\alpha<1,~1<\alpha\leq 2$ and
$\alpha>2$, respectively.
Interestingly, we find that the long-time position distribution in case (ii)
is a function of the scaled variable $x/t^{\phi(\alpha)}$ with an
$\alpha$-dependent scaling function, which has qualitatively very different
shapes for $\alpha<1$ and $\alpha>1$. In contrast, for case (i), the typical
long-time fluctuations of position are Gaussian. | cond-mat_stat-mech |
Latent Heat Calculation of the 3D q=3, 4, and 5 Potts models by Tensor
Product Variational Approach: Three-dimensional (3D) $q$-state Potts models ($q$=3, 4, and 5) are studied
by the tensor product variational approach (TPVA), which is a recently
developed variational method for 3D classical lattice models. The variational
state is given by a two-dimensional (2D) product of local factors, and is
improved by way of self-consistent calculations assisted by the corner transfer
matrix renormalization group (CTMRG). It should be noted that no a priori
condition is imposed for the local factor. Transition temperatures and latent
heats are calculated from the observations of thermodynamic functions in both
ordered and disordered phases. | cond-mat_stat-mech |
Exact analytic multi-quanta states of the Davydov Dimer: The Davydov model describes amide I energy transfer in proteins without
dispersion or dissipation. In spite of five decades of study, there are few
exact analytical results, especially for the discrete version of this model.
Here we develop two methods to determine the exact orthonormal, multi-quanta,
eigenstates of the Davydov dimer. The first method involves the integration of
a system of ordinary differential equations and the second method applies
purely algebraic methods to this problem. We obtain the general expression of
the eigenvalues for any number of quanta and also, as examples, apply the
methods to the detailed derivation of the eigenvectors for one to four quanta,
plus a brief example in the case of $n=5$ and $n=6$. | cond-mat_stat-mech |
Dynamics of Fluctuating Bose-Einstein Condensates: We present a generalized Gross-Pitaevskii equation that describes also the
dissipative dynamics of a trapped partially Bose condensed gas. It takes the
form of a complex nonlinear Schr\"odinger equation with noise. We consider an
approximation to this Langevin field equation that preserves the correct
equilibrium for both the condensed and the noncondensed parts of the gas. We
then use this formalism to describe the reversible formation of a
one-dimensional Bose condensate, and compare with recent experiments. In
addition, we determine the frequencies and the damping of collective modes in
this case. | cond-mat_stat-mech |
Voter Model with Time dependent Flip-rates: We introduce time variation in the flip-rates of the Voter Model. This type
of generalisation is relevant to models of ageing in language change, allowing
the representation of changes in speakers' learning rates over their lifetime
and may be applied to any other similar model in which interaction rates at the
microscopic level change with time. The mean time taken to reach consensus
varies in a nontrivial way with the rate of change of the flip-rates, varying
between bounds given by the mean consensus times for static homogeneous (the
original Voter Model) and static heterogeneous flip-rates. By considering the
mean time between interactions for each agent, we derive excellent estimates of
the mean consensus times and exit probabilities for any time scale of flip-rate
variation. The scaling of consensus times with population size on complex
networks is correctly predicted, and is as would be expected for the ordinary
voter model. Heterogeneity in the initial distribution of opinions has a strong
effect, considerably reducing the mean time to consensus, while increasing the
probability of survival of the opinion which initially occupies the most slowly
changing agents. The mean times to reach consensus for different states are
very different. An opinion originally held by the fastest changing agents has a
smaller chance to succeed, and takes much longer to do so than an evenly
distributed opinion. | cond-mat_stat-mech |
Rayleigh-Benard convection in a hard disk system: We do a generic study of the behavior of a hard disk system under the action
of a thermal gradient in presence of an uniform gravity field. We observe the
conduction-convection transition and measure the main system observables and
fields as the thermal current, global pressure, velocity field, temperature
field,... We can highlight two of the main results of this overall work: (1)
for large enough thermal gradients and a given gravity, we show that the
hydrodynamic fields (density, temperature and velocity) have a natural scaling
form with the gradient. And (2) we show that local equilibrium holds if the
mechanical pressure and the thermodynamic one are not equal, that is, the
Stoke's assumption does not hold in this case. Moreover we observe that the
best fit to the data is obtained when the bulk viscosity depends on the
mechanical pressure. | cond-mat_stat-mech |
On Dynamics and Optimal Number of Replicas in Parallel Tempering
Simulations: We study the dynamics of parallel tempering simulations, also known as the
replica exchange technique, which has become the method of choice for
simulation of proteins and other complex systems. Recent results for the
optimal choice of the control parameter discretization allow a treatment
independent of the system in question. Analyzing mean first passage times
across control parameter space, we find an expression for the optimal number of
replicas in simulations covering a given temperature range. Our results suggest
a particular protocol to optimize the number of replicas in actual simulations. | cond-mat_stat-mech |
Note on Phase Space Contraction and Entropy Production in Thermostatted
Hamiltonian Systems: The phase space contraction and the entropy production rates of Hamiltonian
systems in an external field, thermostatted to obtain a stationary state are
considered. While for stationary states with a constant kinetic energy the two
rates are formally equal for all numbers of particles N, for stationary states
with constant total (kinetic and potential) energy this only obtains for large
N. However, in both cases a large number of particles is required to obtain
equality with the entropy production rate of Irreversible Thermodynamics.
Consequences of this for the positivity of the transport coefficients and for
the Onsager relations are discussed. Numerical results are presented for the
special case of the Lorentz gas. | cond-mat_stat-mech |
Engineering statistical transmutation of identical quantum particles: A fundamental pillar of quantum mechanics concerns indistinguishable quantum
particles. In three dimensions they may be classified into fermions or bosons,
having, respectively, antisymmetric or symmetric wave functions under particle
exchange. One of numerous manifestations of this quantum statistics is the
tendency of fermions (bosons) to anti-bunch (bunch). In a two-particle
scattering experiment with two possible outgoing channels, the probability of
the two particles to arrive each at a different terminal is enhanced (with
respect to classical particles) for fermions, and reduced for bosons. Here we
show that by entangling the particles with an external degree of freedom, we
can engineer quantum statistical transmutation, e.g. causing fermions to bunch.
Our analysis may have consequences on the observed fractional statistics of
anyons, including non-Abelian statistics, with serious implications on quantum
computing operations in the presence of external degrees of freedom. | cond-mat_stat-mech |
A mechanism to synchronize fluctuations in scale free networks using
growth models: In this paper we study the steady state of the fluctuations of the surface
for a model of surface growth with relaxation to any of its lower nearest
neighbors (SRAM) [F. Family, J. Phys. A {\bf 19}, L441 (1986)] in scale free
networks. It is known that for Euclidean lattices this model belongs to the
same universality class as the model of surface relaxation to the minimum
(SRM). For the SRM model, it was found that for scale free networks with
broadness $\lambda$, the steady state of the fluctuations scales with the
system size $N$ as a constant for $\lambda \geq 3$ and has a logarithmic
divergence for $\lambda < 3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf
76}, 046117 (2007)]. It was also shown [La Rocca {\it et al.}, Phys. Rev. E
{\bf 77}, 046120 (2008)] that this logarithmic divergence is due to non-linear
terms that arises from the topology of the network. In this paper we show that
the fluctuations for the SRAM model scale as in the SRM model. We also derive
analytically the evolution equation for this model for any kind of complex
graphs and find that, as in the SRM model, non-linear terms appear due to the
heterogeneity and the lack of symmetry of the network. In spite of that, the
two models have the same scaling, but the SRM model is more efficient to
synchronize systems. | cond-mat_stat-mech |
Sub-Gaussian and subexponential fluctuation-response inequalities: Sub-Gaussian and subexponential distributions are introduced and applied to
study the fluctuation-response relation out of equilibrium. A bound on the
difference in expected values of an arbitrary sub-Gaussian or subexponential
physical quantity is established in terms of its sub-Gaussian or subexponential
norm. Based on that, we find that the entropy difference between two states is
bounded by the energy fluctuation in these states. Moreover, we obtain
generalized versions of the thermodynamic uncertainty relation in different
regimes. Operational issues concerning the application of our results in an
experimental setting are also addressed, and nonasymptotic bounds on the errors
incurred by using the sample mean instead of the expected value in our
fluctuation-response inequalities are derived. | cond-mat_stat-mech |
Noise-intensity fluctuation in Langevin model and its higher-order
Fokker-Planck equation: In this paper, we investigate a Langevin model subjected to stochastic
intensity noise (SIN), which incorporates temporal fluctuations in
noise-intensity. We derive a higher-order Fokker-Planck equation (HFPE) of the
system, taking into account the effect of SIN by the adiabatic elimination
technique. Stationary distributions of the HFPE are calculated by using the
perturbation expansion. We investigate the effect of SIN in three cases: (a)
parabolic and quartic bistable potentials with additive noise, (b) a quartic
potential with multiplicative noise, and (c) a stochastic gene expression
model. We find that the existence of noise intensity fluctuations induces an
intriguing phenomenon of a bimodal-to-trimodal transition in probability
distributions. These results are validated with Monte Carlo simulations. | cond-mat_stat-mech |
Phase diagram of the restricted solid-on-solid model coupled to the
Ising model: We study the phase transitions of a restricted solid-on-solid model coupled
to an Ising model, which can be derived from the coupled XY-Ising model. There
are two kinds of phase transition lines. One is a Ising transition line and the
other is surface roughening transition line. The latter is a KT transition line
from the viewpoint of the XY model. Using a microcanonical Monte Carlo
technique, we obtain a very accurate two dimensional phase diagram. The two
transition lines are separate in all the parameter space we study. This result
is strong evidence that the fully frustrated XY model orders by two separate
transitions and that roughening and reconstruction transitions of crystal
surfaces occur separately. | cond-mat_stat-mech |
Universal entanglement and correlation measure in two-dimensional
conformal field theories: We calculate the amount of entanglement shared by two intervals in the ground
state of a (1+1)-dimensional conformal field theory (CFT), quantified by an
entanglement measure $\mathcal{E}$ based on the computable cross norm (CCNR)
criterion. Unlike negativity or mutual information, we show that $\mathcal{E}$
has a universal expression even for two disjoint intervals, which depends only
on the geometry, the central charge c, and the thermal partition function of
the CFT. We prove this universal expression in the replica approach, where the
Riemann surface for calculating $\mathcal{E}$ at each order n is always a torus
topologically. By analytic continuation, result of n=1/2 gives the value of
$\mathcal{E}$. Furthermore, the results of other values of n also yield
meaningful conclusions: The n=1 result gives a general formula for the
two-interval purity, which enables us to calculate the Renyi-2 N-partite
information for N<=4 intervals; while the $n=\infty$ result bounds the
correlation function of the two intervals. We verify our findings numerically
in the spin-1/2 XXZ chain, whose ground state is described by the Luttinger
liquid. | cond-mat_stat-mech |
Scaling in a Nonconservative Earthquake Model of Self-Organised
Criticality: We numerically investigate the Olami-Feder-Christensen model for earthquakes
in order to characterise its scaling behaviour. We show that ordinary finite
size scaling in the model is violated due to global, system wide events.
Nevertheless we find that subsystems of linear dimension small compared to the
overall system size obey finite (subsystem) size scaling, with universal
critical coefficients, for the earthquake events localised within the
subsystem. We provide evidence, moreover, that large earthquakes responsible
for breaking finite size scaling are initiated predominantly near the boundary. | cond-mat_stat-mech |
Non-Newtonian Poiseuille flow of a gas in a pipe: The Bhatnagar-Gross-Krook kinetic model of the Boltzmann equation is solved
for the steady cylindrical Poiseuille flow fed by a constant gravity field. The
solution is obtained as a perturbation expansion in powers of the field
(through fourth order) and for a general class of repulsive potentials. The
results, which are hardly sensitive to the interaction potential, suggest that
the expansion is only asymptotic. A critical comparison with the profiles
predicted by the Navier-Stokes equations shows that the latter fail over
distances comparable to the mean free path. In particular, while the
Navier-Stokes description predicts a monotonically decreasing temperature as
one moves apart from the cylinder axis, the kinetic theory description shows
that the temperature has a local minimum at the axis and reaches a maximum
value at a distance of the order of the mean free path. Within that distance,
the radial heat flows from the colder to the hotter points, in contrast to what
is expected from the Fourier law. Furthermore, a longitudinal component of the
heat flux exists in the absence of gradients along the longitudinal direction.
Non-Newtonian effects, such as a non uniform hydrostatic pressure and normal
stress differences, are also present. | cond-mat_stat-mech |
Relevant spontaneous magnetization relations for the triangular and the
cubic lattice Ising model: The spontaneous magnetization relations for the 2D triangular and the 3D
cubic lattices of the Ising model are derived by a new tractable easily
calculable mathematical method. The result obtained for the triangular lattice
is compared with the already available result to test and investigate the
relevance the new mathematical method. From this comparison, it is seen that
the agreement of our result is almost the same or almost equivalent to the
previously obtained exact result. The new approach is, then, applied to the
long-standing 3D cubic lattice, and the corresponding expression for the
spontaneous magnetism is derived. The relation obtained is compared with the
already existing numerical results for the 3D lattice. The essence of the
method going to used in this paper is based on exploiting the main
characteristic of the order parameter of a second order phase transition which
provides a more direct physical insight into the calculation of the spontaneous
magnetization of the Ising model. | cond-mat_stat-mech |
Percolation on correlated networks: We reconsider the problem of percolation on an equilibrium random network
with degree-degree correlations between nearest-neighboring vertices focusing
on critical singularities at a percolation threshold. We obtain criteria for
degree-degree correlations to be irrelevant for critical singularities. We
present examples of networks in which assortative and disassortative mixing
leads to unusual percolation properties and new critical exponents. | cond-mat_stat-mech |
Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg
model on the triangulated Kagome (triangles-in-triangles) lattice: The geometric frustration of the spin-1/2 Ising-Heisenberg model on the
triangulated Kagome (triangles-in-triangles) lattice is investigated within the
framework of an exact analytical method based on the generalized star-triangle
mapping transformation. Ground-state and finite-temperature phase diagrams are
obtained along with other exact results for the partition function, Helmholtz
free energy, internal energy, entropy, and specific heat, by establishing a
precise mapping relationship to the corresponding spin-1/2 Ising model on the
Kagome lattice. It is shown that the residual entropy of the disordered spin
liquid phase is for the quantum Ising-Heisenberg model significantly lower than
for its semi-classical Ising limit (S_0/N_T k_B = 0.2806 and 0.4752,
respectively), which implies that quantum fluctuations partially lift a
macroscopic degeneracy of the ground-state manifold in the frustrated regime.
The investigated model system has an obvious relevance to a series of polymeric
coordination compounds Cu_9X_2(cpa)_6 (X=F, Cl, Br and cpa=carboxypentonic
acid) for which we made a theoretical prediction about the temperature
dependence of zero-field specific heat. | cond-mat_stat-mech |
How to Quantify and Avoid Finite Size Effects in Computational Studies
of Crystal Nucleation: The Case of Heterogeneous Ice Nucleation: Computational studies of crystal nucleation can be impacted by finite size
effects, primarily due to unphysical interactions between crystalline nuclei
and their periodic images. It is, however, not always feasible to
systematically investigate the sensitivity of nucleation kinetics and mechanism
to system size due to large computational costs of nucleation studies. Here, we
use jumpy forward flux sampling to accurately compute the rates of
heterogeneous ice nucleation in the vicinity of square-shaped model
structureless ice nucleating particles (INPs) of different sizes, and identify
three distinct regimes for the dependence of rate on the INP dimension, $L$.
For small INPs, the rate is a strong function of $L$ due to artificial spanning
of critical nuclei across the periodic boundary. Intermediate-sized INPs,
however, give rise to the emergence of non-spanning 'proximal` nuclei that are
close enough to their periodic images to fully structure the intermediary
liquid. While such proximity can facilitate nucleation, its effect is offset by
the higher density of the intermediary liquid, leading to artificially small
nucleation rates overall. The critical nuclei formed at large INPs are neither
spanning nor proximal. Yet, the rate is a weak function of $L$, with its
logarithm scaling linearly with $1/L$. The key heuristic emerging from these
observations is that finite size effects will be minimal if critical nuclei are
neither spanning nor proximal, and if the intermediary liquid has a region that
is structurally indistinguishable from the supercooled liquid under the same
conditions. | cond-mat_stat-mech |
Equilibrium statistics of an inelastically bouncing ball, subject to
gravity and a random force: We consider a particle moving on the half line $x>0$ and subject to a
constant force in the $-x$ direction plus a delta-correlated random force. At
$x=0$ the particle is reflected inelastically. The velocities just after and
before reflection satisfy $v_f=-rv_i$, where $r$ is the coefficient of
restitution. This simple model is of interest in connection with studies of
driven granular matter in a gravitational field. With an exact analytical
approach and simulations we study the steady state distribution function
$P(x,v)$. | cond-mat_stat-mech |
Screening of classical Casimir forces by electrolytes in semi-infinite
geometries: We study the electrostatic Casimir effect and related phenomena in
equilibrium statistical mechanics of classical (non-quantum) charged fluids.
The prototype model consists of two identical dielectric slabs in empty space
(the pure Casimir effect) or in the presence of an electrolyte between the
slabs. In the latter case, it is generally believed that the long-ranged
Casimir force due to thermal fluctuations in the slabs is screened by the
electrolyte into some residual short-ranged force. The screening mechanism is
based on a "separation hypothesis": thermal fluctuations of the electrostatic
field in the slabs can be treated separately from the pure image effects of the
"inert" slabs on the electrolyte particles. In this paper, by using a
phenomenological approach under certain conditions, the separation hypothesis
is shown to be valid. The phenomenology is tested on a microscopic model in
which the conducting slabs and the electrolyte are modelled by the symmetric
Coulomb gases of point-like charges with different particle fugacities. The
model is solved in the high-temperature Debye-H\"uckel limit (in two and three
dimensions) and at the free fermion point of the Thirring representation of the
two-dimensional Coulomb gas. The Debye-H\"uckel theory of a Coulomb gas between
dielectric walls is also solved. | cond-mat_stat-mech |
Q-factor: A measure of competition between the topper and the average in
percolation and in SOC: We define the $Q$-factor in the percolation problem as the quotient of the
size of the largest cluster and the average size of all clusters. As the
occupation probability $p$ is increased, the $Q$-factor for the system size $L$
grows systematically to its maximum value $Q_{max}(L)$ at a specific value
$p_{max}(L)$ and then gradually decays. Our numerical study of site percolation
problems on the square, triangular and the simple cubic lattices exhibits that
the asymptotic values of $p_{max}$ though close, are distinctly different from
the corresponding percolation thresholds of these lattices. We have also shown
using the scaling analysis that at $p_{max}$ the value of $Q_{max}(L)$ diverges
as $L^d$ ($d$ denoting the dimension of the lattice) as the system size
approaches to their asymptotic limit. We have further extended this idea to the
non-equilibrium systems such as the sandpile model of self-organized
criticality. Here, the $Q(\rho,L)$-factor is the quotient of the size of the
largest avalanche and the cumulative average of the sizes of all the
avalanches; $\rho$ being the drop density of the driving mechanism. This study
has been prompted by some observations in Sociophysics. | cond-mat_stat-mech |
Comment on ``Renormalization-group picture of the Lifshitz critical
behavior'': We show that the recent renormalization-group analysis of Lifshitz critical
behavior presented by Leite [Phys. Rev. B {\bf 67}, 104415 (2003)] suffers from
a number of severe deficiencies. In particular, we show that his approach does
not give an ultraviolet finite renormalized theory, is plagued by
inconsistencies, misses the existence of a nontrivial anisotropy exponent
$\theta\ne 1/2$, and therefore yields incorrect hyperscaling relations. His
$\epsilon$-expansion results to order $\epsilon^2$ for the critical exponents
of $m$-axial Lifshitz points are incorrect both in the anisotropic ($0<m<d$)
and the isotropic cases ($m=d$). The inherent inconsistencies and the lack of a
sound basis of the approach makes its results unacceptable even if they are
interpreted in the sense of approximations. | cond-mat_stat-mech |
Understanding and Controlling Regime Switching in Molecular Diffusion: Diffusion can be strongly affected by ballistic flights (long jumps) as well
as long-lived sticking trajectories (long sticks). Using statistical inference
techniques in the spirit of Granger causality, we investigate the appearance of
long jumps and sticks in molecular-dynamics simulations of diffusion in a
prototype system, a benzene molecule on a graphite substrate. We find that
specific fluctuations in certain, but not all, internal degrees of freedom of
the molecule can be linked to either long jumps or sticks. Furthermore, by
changing the prevalence of these predictors with an outside influence, the
diffusion of the molecule can be controlled. The approach presented in this
proof of concept study is very generic, and can be applied to larger and more
complex molecules. Additionally, the predictor variables can be chosen in a
general way so as to be accessible in experiments, making the method feasible
for control of diffusion in applications. Our results also demonstrate that
data-mining techniques can be used to investigate the phase-space structure of
high-dimensional nonlinear dynamical systems. | cond-mat_stat-mech |
Diffusion in a logarithmic potential: scaling and selection in the
approach to equilibrium: The equation which describes a particle diffusing in a logarithmic potential
arises in diverse physical problems such as momentum diffusion of atoms in
optical traps, condensation processes, and denaturation of DNA molecules. A
detailed study of the approach of such systems to equilibrium via a scaling
analysis is carried out, revealing three surprising features: (i) the solution
is given by two distinct scaling forms, corresponding to a diffusive (x ~
\sqrt{t}) and a subdiffusive (x >> \sqrt{t}) length scales, respectively; (ii)
the scaling exponents and scaling functions corresponding to both regimes are
selected by the initial condition; and (iii) this dependence on the initial
condition manifests a "phase transition" from a regime in which the scaling
solution depends on the initial condition to a regime in which it is
independent of it. The selection mechanism which is found has many similarities
to the marginal stability mechanism which has been widely studied in the
context of fronts propagating into unstable states. The general scaling forms
are presented and their practical and theoretical applications are discussed. | cond-mat_stat-mech |
Analytical theory of mesoscopic Bose-Einstein condensation in ideal gas: We find universal structure and scaling of BEC statistics and thermodynamics
for mesoscopic canonical-ensemble ideal gas in a trap for any parameters,
including critical region. We identify universal constraint-cut-off mechanism
that makes BEC fluctuations non-Gaussian and is responsible for critical
phenomena. Main result is analytical solution to problem of critical phenomena.
It is derived by calculating universal distribution of noncondensate occupation
(Landau function) and then universal functions for physical quantities. We find
asymptotics of that solution and its approximations which describe universal
structure of critical region in terms of parabolic cylinder or confluent
hypergeometric functions. Results for order parameter, statistics, and
thermodynamics match known asymptotics outside critical region. We suggest
2-level and 3-level trap models and find their exact solutions in terms of
cut-off negative binomial distribution (that tends to cut-off gamma
distribution in continuous limit) and confluent hypergeometric distribution. We
introduce a regular refinement scheme for condensate statistics approximations
on the basis of infrared universality of higher-order cumulants and method of
superposition and show how to model BEC statistics in actual traps. We find
that 3-level trap model with matching the first 4 or 5 cumulants is enough to
yield remarkably accurate results in whole critical region. We derive exact
multinomial expansion for noncondensate occupation distribution and find its
high temperature asymptotics (Poisson distribution). We demonstrate that
critical exponents and a few known terms of Taylor expansion of universal
functions, calculated previously from fitting finite-size simulations within
renorm-group theory, can be obtained from presented solutions. | cond-mat_stat-mech |
The Coulomb-Higgs phase transition of three-dimensional lattice
Abelian-Higgs gauge models with noncompact gauge variables and gauge fixing: We study the critical behavior of three-dimensional (3D) lattice
Abelian-Higgs (AH) gauge models with noncompact gauge variables and
multicomponent complex scalar fields, along the transition line between the
Coulomb and Higgs phases. Previous works that focused on gauge-invariant
correlations provided evidence that, for a sufficiently large number of scalar
components, these transitions are continuous and associated with the stable
charged fixed point of the renormalization-group flow of the 3D AH field theory
(scalar electrodynamics), in which charged scalar matter is minimally coupled
with an electromagnetic field. Here we extend these studies by considering
gauge-dependent correlations of the gauge and matter fields, in the presence of
two different gauge fixings, the Lorenz and the axial gauge fixing. Our results
for N=25 are definitely consistent with the predictions of the AH field theory
and therefore provide additional evidence for the characterization of the 3D AH
transitions along the Coulomb-Higgs line as charged transitions in the AH
field-theory universality class. Moreover, our results give additional insights
on the role of the gauge fixing at charged transitions. In particular, we show
that scalar correlations are critical only if a hard Lorenz gauge fixing is
imposed. | cond-mat_stat-mech |
Asymptotic front behavior in an $A+B\rightarrow 2A$ reaction under
subdiffusion: We discuss the front propagation in the $A+B\rightarrow 2A$ reaction under
subdiffusion which is described by continuous time random walks with a
heavy-tailed power law waiting time probability density function. Using a
crossover argument, we discuss the two scaling regimes of the front
propagation: an intermediate asymptotic regime given by the front solution of
the corresponding continuous equation, and the final asymptotics, which is
fluctuation-dominated and therefore lays out of reach of the continuous scheme.
We moreover show that the continuous reaction subdiffusion equation indeed
possesses a front solution that decelerates and becomes narrow in the course of
time. This continuous description breaks down for larger times when the front
gets atomically sharp. We show that the velocity of such fronts decays in time
faster than in the continuous regime. | cond-mat_stat-mech |
Consistent Lattice Boltzmann Method: The problem of energy conservation in the lattice Boltzmann method is solved.
A novel model with energy conservation is derived from Boltzmann's kinetic
theory. It is demonstrated that the full thermo-hydrodynamics pertinent to the
Boltzmann equation is recovered in the domain where variations around the
reference temperature are small. Simulation of a Poiseuille micro-flow is
performed in a quantitative agreement with exact results for low and moderate
Knudsen numbers. The new model extends in a natural way the standard lattice
Boltzmann method to a thermodynamically consistent simulation tool for
nearly-incompressible flows. | cond-mat_stat-mech |
Kondo signature in heat transfer via a local two-state system: We study the Kondo effect in heat transport via a local two-state system.
This system is described by the spin-boson Hamiltonian with Ohmic dissipation,
which can be mapped onto the Kondo model with anisotropic exchange coupling. We
calculate thermal conductance by the Monte Carlo method based on the exact
formula. Thermal conductance has a scaling form \kappa = (k_B^2 T_K/\hbar)
f(\alpha,T/T_K ), where T_K and \alpha indicate the Kondo temperature and
dimensionless coupling strength, respectively. Temperature dependence of
conductance is classified by the Kondo temperature as \kappa\propto (T/T_K )^3
for T\ll T_K and \kappa\propto (k_B T / \hbar\omega_c)^{2\alpha-1} for T\gg
T_K. Similarities to the Kondo signature in electric transport are discussed. | cond-mat_stat-mech |
Microcanonical Thermostatistical Investigation of the Blackbody
Radiation: In this work is presented the microcanonical analysis of the blackbody
radiation. In our model the electromagnetic radiation is confined in an
isolated container with volume V in which the radiation can not escape,
conserving this way its total energy, E. Our goal is to precise the meaning of
the Thermodynamic Limit for this system as well as the description of the
nonextensive effects of the generalized Planck formula for the spectral density
of energy. Our analysis shows the sterility of the intents of finding
nonnextensive effects in normal conditions: the traditional description of the
blackbody radiation is extraordinarily exact. The nonextensive effects only
appear in the low temperature region, however, they are extremely difficult to
detect. | cond-mat_stat-mech |
Informational and Causal Architecture of Continuous-time Renewal and
Hidden Semi-Markov Processes: We introduce the minimal maximally predictive models ({\epsilon}-machines) of
processes generated by certain hidden semi-Markov models. Their causal states
are either hybrid discrete-continuous or continuous random variables and
causal-state transitions are described by partial differential equations.
Closed-form expressions are given for statistical complexities, excess
entropies, and differential information anatomy rates. We present a complete
analysis of the {\epsilon}-machines of continuous-time renewal processes and,
then, extend this to processes generated by unifilar hidden semi-Markov models
and semi-Markov models. Our information-theoretic analysis leads to new
expressions for the entropy rate and the rates of related information measures
for these very general continuous-time process classes. | cond-mat_stat-mech |
Negative Specific Heat in a Quasi-2D Generalized Vorticity Model: Negative specific heat is a dramatic phenomenon where processes decrease in
temperature when adding energy. It has been observed in gravo-thermal collapse
of globular clusters. We now report finding this phenomenon in bundles of
nearly parallel, periodic, single-sign generalized vortex filaments in the
electron magnetohydrodynamic (EMH) model for the unbounded plane under strong
magnetic confinement. We derive the specific heat using a steepest descent
method and a mean field property. Our derivations show that as temperature
increases, the overall size of the system increases exponentially and the
energy drops. The implication of negative specific heat is a runaway reaction,
resulting in a collapsing inner core surrounded by an expanding halo of
filaments. | cond-mat_stat-mech |
Analytical approximation for reaction-diffusion processes in rough pores: The concept of an active zone in Laplacian transport is used to obtain an
analytical approximation for the reactive effectiveness of a pore with an
arbitrary rough geometry. We show that this approximation is in very good
agreement with direct numerical simulations performed over a wide range of
diffusion-reaction conditions (i.e., with or without screening effects). In
particular, we find that in most practical situations, the effect of roughness
is to increase the intrinsic reaction rate by a geometrical factor, namely, the
ratio between the real and the apparent surface area. We show that this simple
geometrical information is sufficient to characterize the reactive
effectiveness of a pore, in spite of the complex morphological features it
might possess. | cond-mat_stat-mech |
Out-of-equilibrium scaling behavior arising during round-trip protocols
across a quantum first-order transition: We investigate the nonequilibrium dynamics of quantum spin chains during a
round-trip protocol that slowly drives the system across a quantum first-order
transition. Out-of-equilibrium scaling behaviors \`a la Kibble-Zurek for the
single-passage protocol across the first-order transition have been previously
determined. Here, we show that such scaling relations persist when the driving
protocol is inverted and the transition is approached again by a
far-from-equilibrium state. This results in a quasi-universality of the scaling
functions, which keep some dependence on the details of the protocol at the
inversion time. We explicitly determine such quasi-universal scaling functions
by employing an effective two-level description of the many-body system near
the transition. We discuss the validity of this approximation and how this
relates to the observed scaling regime. Although our results apply to generic
systems, we focus on the prototypical example of a $1D$ transverse field Ising
model in the ferromagnetic regime, which we drive across the first-order
transitions through a time-dependent longitudinal field. | cond-mat_stat-mech |
Exact Solution of a Vertex Model with Unlimited Number of States Per
Bond: The exact solution is obtained for the eigenvalues and eigenvectors of the
row-to-row transfer matrix of a two-dimensional vertex model with unlimited
number of states per bond. This model is a classical counterpart of a quantum
spin chain with an unlimited value of spin. This quantum chain is studied using
general predictions of conformal field theory. The long-distance behaviour of
some ground-state correlation functions is derived from a finite-size analysis
of the gapless excitations. | cond-mat_stat-mech |
On the velocity distributions of the one-dimensional inelastic gas: We consider the single-particle velocity distribution of a one-dimensional
fluid of inelastic particles. Both the freely evolving (cooling) system and the
non-equilibrium stationary state obtained in the presence of random forcing are
investigated, and special emphasis is paid to the small inelasticity limit. The
results are obtained from analytical arguments applied to the Boltzmann
equation along with three complementary numerical techniques (Molecular
Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of
integro-differential kinetic equations). For the freely cooling fluid, we
investigate in detail the scaling properties of the bimodal velocity
distribution emerging close to elasticity and calculate the scaling function
associated with the distribution function. In the heated steady state, we find
that, depending on the inelasticity, the distribution function may display two
different stretched exponential tails at large velocities. The inelasticity
dependence of the crossover velocity is determined and it is found that the
extremely high velocity tail may not be observable at ``experimentally
relevant'' inelasticities. | cond-mat_stat-mech |
Characterization of relaxation processes in interacting vortex matter
through a time-dependent correlation length: Vortex lines in type-II superconductors display complicated relaxation
processes due to the intricate competition between their mutual repulsive
interactions and pinning to attractive point or extended defects. We perform
extensive Monte Carlo simulations for an interacting elastic line model with
either point-like or columnar pinning centers. From measurements of the space-
and time-dependent height-height correlation function for lateral flux line
fluctuations, we extract a characteristic correlation length that we use to
investigate different non-equilibrium relaxation regimes. The specific time
dependence of this correlation length for different disorder configurations
displays characteristic features that provide a novel diagnostic tool to
distinguish between point-like pinning centers and extended columnar defects. | cond-mat_stat-mech |
High-precision Estimate of the Critical Exponents for the Directed Ising
Universality Class: With extensive Monte Carlo simulations, we present high-precision estimates
of the critical exponents of branching annihilating random walks with two
offspring, a prototypical model of the directed Ising universality class in one
dimension. To estimate the exponents accurately, we propose a systematic method
to find corrections to scaling whose leading behavior is supposed to take the
form $t^{-\chi}$ in the long-time limit at the critical point. Our study shows
that $\chi\approx 0.75$ for the number of particles in defect simulations and
$\chi \approx 0.5$ for other measured quantities, which should be compared with
the widely used value of $\chi = 1$. Using $\chi$ so obtained, we analyze the
effective exponents to find that $\beta/\nu_\| = 0.2872(2)$, $z = 1.7415(5)$,
$\eta = 0.0000(2)$, and accordingly, $\beta /\nu_\perp = 0.5000(6)$. Our
numerical results for $\beta/\nu_\|$ and $z$ are clearly different from the
conjectured rational numbers $\beta/\nu_\| = \frac{2}{7} \approx 0.2857$, $z =
\frac{7}{4}= 1.75$ by Jensen [Phys. Rev. E, {\bf 50}, 3623 (1994)]. Our result
for $\beta/\nu_\perp$, however, is consistent with $\frac{1}{2}$, which is
believed to be exact. | cond-mat_stat-mech |
Kinetics of Vapor-Solid Phase Transitions: Structure, growth and
mechanism: Kinetics of separation between the low and high density phases in a single
component Lennard-Jones model has been studied via molecular dynamics
simulations, at a very low temperature, in the space dimension $d=2$. For
densities close to the vapor (low density) branch of the coexistence curve,
disconnected clusters of the high density phase exhibit ballistic motion, the
kinetic energy distribution of the clusters being closely Maxwellian. Starting
from nearly circular shapes, at the time of nucleation, these clusters grow via
sticky collisions, gaining filament-like nonequilibrium structure at late
times, with a very low fractal dimensionality. The origin of the latter is
shown to lie in the low mobility of the constituent particles, in the
corresponding cluster reference frame, due to the (quasi-long-range)
crystalline order. Standard self-similarity in the domain pattern, typically
observed in kinetics of phase transitions, is found to be absent in this growth
process. This invalidates the common method, that provides a growth law same as
in immiscible solid mixtures, of quantifying growth. An appropriate alternative
approach, involving the fractality in the structure, quantifies the growth of
the characteristic "length" to be a power-law with time, the exponent being
surprisingly high. The observed growth law has been derived via a
nonequilibrium kinetic theory. | cond-mat_stat-mech |
Time evolution of entanglement entropy after quenches in two-dimensional
free fermion systems: a dimensional reduction treatment: We study the time evolution of the R\'enyi entanglement entropies following a
quantum quench in a two-dimensional (2D) free-fermion system. By employing
dimensional reduction, we effectively transform the 2D problem into decoupled
chains, a technique applicable when the system exhibits translational
invariance in one direction. Various initial configurations are examined,
revealing that the behavior of entanglement entropies can often be explained by
adapting the one-dimensional quasiparticle picture. However, intriguingly, for
specific initial states the entanglement entropy saturates to a finite value
without the reduced density matrix converging to a stationary state. We discuss
the conditions necessary for a stationary state to exist and delve into the
necessary modifications to the quasiparticle picture when such a state is
absent. | cond-mat_stat-mech |
Far-from-equilibrium growth of thin films in a temperature gradient: The irreversible growth of thin films under far-from-equilibrium conditions
is studied in $(2+1)-$dimensional strip geometries. Across one of the
transverse directions, a temperature gradient is applied by thermal baths at
fixed temperatures between $T_1$ and $T_2$, where $T_1<T_c^{hom}<T_2$ and
$T_c^{hom}=0.69(1)$ is the critical temperature of the system in contact with
an homogeneous thermal bath. By using standard finite-size scaling methods, we
characterized a continuous order-disorder phase transition driven by the
thermal bath gradient with critical temperature $T_c=0.84(2)$ and critical
exponents $\nu=1.53(6)$, $\gamma=2.54(11)$, and $\beta=0.26(8)$, which belong
to a different universality class from that of films grown in an homogeneous
bath. Furthermore, the effects of the temperature gradient are analyzed by
means of a bond model that captures the growth dynamics. The interplay of
geometry and thermal bath asymmetries leads to growth bond flux asymmetries and
the onset of transverse ordering effects that explain qualitatively the shift
in the critical temperature. | cond-mat_stat-mech |
Aging and fluctuation-dissipation ratio for the diluted Ising Model: We consider the out-of-equilibrium, purely relaxational dynamics of a weakly
diluted Ising model in the aging regime at criticality. We derive at first
order in a $\sqrt{\epsilon}$ expansion the two-time response and correlation
functions for vanishing momenta. The long-time limit of the critical
fluctuation-dissipation ratio is computed at the same order in perturbation
theory. | cond-mat_stat-mech |
Scaling, Multiscaling, and Nontrivial Exponents in Inelastic Collision
Processes: We investigate velocity statistics of homogeneous inelastic gases using the
Boltzmann equation. Employing an approximate uniform collision rate, we obtain
analytic results valid in arbitrary dimension. In the freely evolving case, the
velocity distribution is characterized by an algebraic large velocity tail,
P(v,t) ~ v^{-sigma}. The exponent sigma(d,epsilon), a nontrivial root of an
integral equation, varies continuously with the spatial dimension, d, and the
dissipation coefficient, epsilon. Although the velocity distribution follows a
scaling form, its moments exhibit multiscaling asymptotic behavior.
Furthermore, the velocity autocorrelation function decays algebraically with
time, A(t)=<v(0)v(t)> ~ t^{-alpha}, with a non-universal dissipation-dependent
exponent alpha=1/epsilon. In the forced case, the steady state Fourier
transform is obtained via a cumulant expansion. Even in this case, velocity
correlations develop and the velocity distribution is non-Maxwellian. | cond-mat_stat-mech |
Large-n conditional facedness m_n of 3D Poisson-Voronoi cells: We consider the three-dimensional Poisson-Voronoi tessellation and study the
average facedness m_n of a cell known to neighbor an n-faced cell. Whereas
Aboav's law states that m_n=A+B/n, theoretical arguments indicate an asymptotic
expansion m_n = 8 + k_1 n^{-1/6} +.... Recent new Monte Carlo data due to Lazar
et al., based on a very large data set, now clearly rule out Aboav's law. In
this work we determine the numerical value of k_1 and compare the expansion to
the Monte Carlo data. The calculation of k_1 involves an auxiliary planar
cellular structure composed of circular arcs, that we will call the
Poisson-Moebius diagram. It is a special case of more general Moebius diagrams
(or multiplicatively weighted power diagrams) and is of interest for its own
sake. We obtain exact results for the total edge length per unit area, which is
a prerequisite for the coefficient k_1, and a few other quantities in this
diagram. | cond-mat_stat-mech |
1/f Noise and Extreme Value Statistics: We study the finite-size scaling of the roughness of signals in systems
displaying Gaussian 1/f power spectra. It is found that one of the extreme
value distributions (Gumbel distribution) emerges as the scaling function when
the boundary conditions are periodic. We provide a realistic example of
periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution
is a good approximation for the case of nonperiodic boundary conditions as
well. Experiments on voltage fluctuations in GaAs films are analyzed and
excellent agreement is found with the theory. | cond-mat_stat-mech |
Magnetic properties of exactly solvable doubly decorated
Ising-Heisenberg planar models: Applying the decoration-iteration procedure, we introduce a class of exactly
solvable doubly decorated planar models consisting both of the Ising- and
Heisenberg-type atoms. Exact solutions for the ground state, phase diagrams and
basic physical quantities are derived and discussed. The detailed analysis of
the relevant quantities suggests the existence of an interesting quantum
antiferromagnetic phase in the system. | cond-mat_stat-mech |
Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model: The equilibrium phase behavior of microphase-forming substances and models is
notoriously difficult to obtain because of the extended metastability of the
modulated phases. We develop a simulation method based on thermodynamic
integration that avoids this problem and with which we obtain the phase diagram
of the canonical three-dimensional axial next-nearest-neighbor Ising model. The
equilibrium devil's staircase, magnetization, and susceptibility are obtained.
The critical exponents confirm the XY nature of the disorder-modulated phase
transition beyond the Lifshitz point. The results identify the limitations of
various approximation schemes used to analyze this basic microphase-forming
model. | cond-mat_stat-mech |
On the Truncation of Systems with Non-Summable Interactions: In this note we consider long range $q$-states Potts models on
$\mathbf{Z}^d$, $d\geq 2$. For various families of non-summable ferromagnetic
pair potentials $\phi(x)\geq 0$, we show that there exists, for all inverse
temperature $\beta>0$, an integer $N$ such that the truncated model, in which
all interactions between spins at distance larger than $N$ are suppressed, has
at least $q$ distinct infinite-volume Gibbs states. This holds, in particular,
for all potentials whose asymptotic behaviour is of the type $\phi(x)\sim
\|x\|^{-\alpha}$, $0\leq\alpha\leq d$. These results are obtained using simple
percolation arguments. | cond-mat_stat-mech |
Emergence of oscillations in fixed energy sandpile models on complex
networks: Fixed-energy sandpile (FES) models, introduced to understand the
self-organized criticality, show a continuous phase transition between
absorbing and active phases. In this work, we study the dynamics of the
deterministic FES models on random networks. We observe that close to absorbing
transition the density of active nodes oscillates and nodes topple in
synchrony. The deterministic toppling rule and the small-world property of
random networks lead to the emergence of sustained oscillations. The amplitude
of oscillations becomes larger with increasing the value of network randomness.
The bifurcation diagram for the density of active nodes is obtained. We use the
activity-dependent rewiring rule and show that the interplay between the
network structure and the FES dynamics leads to the emergence of a bistable
region with a first-order transition between the absorbing and active states.
Furthermore during the rewiring, the ordered activation pattern of the nodes is
broken, which causes the oscillations to disappear. | cond-mat_stat-mech |
Self-Organized Criticality in the Olami-Feder-Christensen model: A system is in a self-organized critical state if the distribution of some
measured events (avalanche sizes, for instance) obeys a power law for as many
decades as it is possible to calculate or measure. The finite-size scaling of
this distribution function with the lattice size is usually enough to assume
that any cut off will disappear as the lattice size goes to infinity. This
approach, however, can lead to misleading conclusions. In this work we analyze
the behavior of the branching rate sigma of the events to establish whether a
system is in a critical state. We apply this method to the
Olami-Feder-Christensen model to obtain evidences that, in contrast to previous
results, the model is critical in the conservative regime only. | cond-mat_stat-mech |
Geometrical interpretation of fluctuating hydrodynamics in diffusive
systems: We discuss geometric formulations of hydrodynamic limits in diffusive
systems. Specifically, we describe a geometrical construction in the space of
density profiles --- the Wasserstein geometry --- which allows the
deterministic hydrodynamic evolution of the systems to be related to steepest
descent of the free energy, and show how this formulation can be related to
most probable paths of mesoscopic dissipative systems. The geometric viewpoint
is also linked to fluctuating hydrodynamics of these systems via a saddle point
argument. | cond-mat_stat-mech |
Interface growth in two dimensions: A Loewner-equation approach: The problem of Laplacian growth in two dimensions is considered within the
Loewner-equation framework. Initially the problem of fingered growth recently
discussed by Gubiec and Szymczak [T. Gubiec and P. Szymczak, Phys. Rev. E 77,
041602 (2008)] is revisited and a new exact solution for a three-finger
configuration is reported. Then a general class of growth models for an
interface growing in the upper-half plane is introduced and the corresponding
Loewner equation for the problem is derived. Several examples are given
including interfaces with one or more tips as well as multiple growing
interfaces. A generalization of our interface growth model in terms of
``Loewner domains,'' where the growth rule is specified by a time evolving
measure, is briefly discussed. | cond-mat_stat-mech |
Slow relaxation, dynamic transitions and extreme value statistics in
disordered systems: We show that the dynamics of simple disordered models, like the directed Trap
Model and the Random Energy Model, takes place at a coexistence point between
active and inactive dynamical phases. We relate the presence of a dynamic phase
transition in these models to the extreme value statistics of the associated
random energy landscape. | cond-mat_stat-mech |
Conductance in diffusive quasi-one-dimensional periodic waveguides: a
semiclassical and random matrix study: We study quantum transport properties of finite periodic
quasi-one-dimensional waveguides whose classical dynamics is diffusive. The
system we consider is a scattering configuration, composed of a finite periodic
chain of $L$ identical (classically chaotic and finite-horizon) unit cells,
which is connected to semi-infinite plane leads at its extremes. Particles
inside the cavity are free and only interact with the boundaries through
elastic collisions; this means waves are described by the Helmholtz equation
with Dirichlet boundary conditions on the waveguide walls. The equivalent to
the disorder ensemble is an energy ensemble, defined over a classically small
range but many mean level spacings wide. The number of propagative channels in
the leads is $N$. We have studied the (adimensional) Landauer conductance $g$
as a function of $L$ and $N$ in the cosine-shaped waveguide and by means of our
RMT periodic chain model. We have found that $<g(L)>$ exhibit two regimes.
First, for chains of length $L\lesssim\sqrt{N}$ the dynamics is diffusive just
like in the disordered wire in the metallic regime, where the typic ohmic
scaling is observed with $<g(L)> = N/(L+1)$. In this regime, the conductance
distribution is a Gaussian with small variance but which grows linearly with
$L$. Then, in longer systems with $L\gg\sqrt{N}$, the periodic nature becomes
relevant and the conductance reaches a constant asymptotic value
$<g(L\to\infty)> \sim <N_B>$. The variance approaches a constant value
$\sim\sqrt{N}$ as $L\to\infty$. Comparing the conductance using the unitary and
orthogonal circular ensembles we observed that a weak localization effect is
present in the two regimes. | 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 |
Colossal Brownian yet non-Gaussian diffusion induced by nonequilibrium
noise: We report on novel Brownian, yet non-Gaussian diffusion, in which the mean
square displacement of the particle grows linearly with time, the probability
density for the particle spreading is Gaussian-like, however, the probability
density for its position increments possesses an exponentially decaying tail.
In contrast to recent works in this area, this behaviour is not a consequence
of either a space or time-dependent diffusivity, but is induced by external
non-thermal noise acting on the particle dwelling in a periodic potential. The
existence of the exponential tail in the increment statistics leads to colossal
enhancement of diffusion, surpassing drastically the previously researched
situation known under the label of "giant" diffusion. This colossal diffusion
enhancement crucially impacts a broad spectrum of the first arrival problems,
such as diffusion limited reactions governing transport in living cells. | cond-mat_stat-mech |
Improved upper and lower energy bounds for antiferromagnetic Heisenberg
spin systems: Large spin systems as given by magnetic macromolecules or two-dimensional
spin arrays rule out an exact diagonalization of the Hamiltonian. Nevertheless,
it is possible to derive upper and lower bounds of the minimal energies, i.e.
the smallest energies for a given total spin S.
The energy bounds are derived under additional assumptions on the topology of
the coupling between the spins. The upper bound follows from "n-cyclicity",
which roughly means that the graph of interactions can be wrapped round a ring
with n vertices. The lower bound improves earlier results and follows from
"n-homogeneity", i.e. from the assumption that the set of spins can be
decomposed into n subsets where the interactions inside and between spins of
different subsets fulfill certain homogeneity conditions. Many Heisenberg spin
systems comply with both concepts such that both bounds are available.
By investigating small systems which can be numerically diagonalized we find
that the upper bounds are considerably closer to the true minimal energies than
the lower ones. | cond-mat_stat-mech |
Triangular arbitrage as an interaction among foreign exchange rates: We first show that there are in fact triangular arbitrage opportunities in
the spot foreign exchange markets, analyzing the time dependence of the
yen-dollar rate, the dollar-euro rate and the yen-euro rate. Next, we propose a
model of foreign exchange rates with an interaction. The model includes effects
of triangular arbitrage transactions as an interaction among three rates. The
model explains the actual data of the multiple foreign exchange rates well. | cond-mat_stat-mech |
Triangle Distribution and Equation of State for Classical Rigid Disks: The triangle distribution function f^(3) for three mutual nearest neighbors
in the plane describes basic aspects of short-range order and statistical
thermodynamics in two-dimensional many-particle systems. This paper examines
prospects for constructing a self-consistent calculation for the rigid-disk
system f^(3). We present several identities obeyed by f^(3). A rudimentary
closure suggested by scaled-particle theory is introduced. In conjunction with
three of the basic identities, this closure leads to a unique f^(3) over the
entire density range. The pressure equation of state exhibits qualitatively
correct behavior in both the low density and the close-packed limits, but no
intervening phase transition appears. We discuss extensions to improved disk
closures, and to the three-dimensional rigid sphere system. | cond-mat_stat-mech |
Metal - non-metal transition and the second critical point in expanded
metals: Based on the non-relativistic Coulomb model within which the matter is a
system of interacting electrons and nuclei, using the quantum field theory and
linear response theory methods, opportunity for the existence of the second
critical point in expanded metals, which is directly related to the
metal--nonmetal transition, predicted by Landau and Zeldovitch, is
theoretically justified. It is shown that the matter at the second critical
point is in the state of true dielectric with zero static conductivity. The
results obtained are in agreement with recent experiments for expanded metals.
The existence of the second critical point is caused by the initial
multi-component nature of the matter consisting of electrons and nuclei and the
long-range character of the Coulomb interaction. (Accepted in PTEP) | cond-mat_stat-mech |
A simple one-dimensional model of heat conduction which obeys Fourier's
law: We present the computer simulation results of a chain of hard point particles
with alternating masses interacting on its extremes with two thermal baths at
different temperatures. We found that the system obeys Fourier's law at the
thermodynamic limit. This result is against the actual belief that one
dimensional systems with momentum conservative dynamics and nonzero pressure
have infinite thermal conductivity. It seems that thermal resistivity occurs in
our system due to a cooperative behavior in which light particles tend to
absorb much more energy than the heavier ones. | cond-mat_stat-mech |
Random graphs containing arbitrary distributions of subgraphs: Traditional random graph models of networks generate networks that are
locally tree-like, meaning that all local neighborhoods take the form of trees.
In this respect such models are highly unrealistic, most real networks having
strongly non-tree-like neighborhoods that contain short loops, cliques, or
other biconnected subgraphs. In this paper we propose and analyze a new class
of random graph models that incorporates general subgraphs, allowing for
non-tree-like neighborhoods while still remaining solvable for many fundamental
network properties. Among other things we give solutions for the size of the
giant component, the position of the phase transition at which the giant
component appears, and percolation properties for both site and bond
percolation on networks generated by the model. | cond-mat_stat-mech |
Crossing the bottleneck of rain formation: The demixing of a binary fluid mixture, under gravity, is a two stage
process. Initially droplets, or in general aggregates, grow diffusively by
collecting supersaturation from the bulk phase. Subsequently, when the droplets
have grown to a size, where their Peclet number is of order unity, buoyancy
substantially enhances droplet growth. The dynamics approaches a finite-time
singularity where the droplets are removed from the system by precipitation.
The two growth regimes are separated by a bottleneck of minimal droplet growth.
Here, we present a low-dimensional model addressing the time span required to
cross the bottleneck, and we hence determine the time, \Delta t, from initial
droplet growth to rainfall. Our prediction faithfully captures the dependence
of \Delta t on the ramp rate of the droplet volume fraction, \xi, the droplet
number density, the interfacial tension, the mass diffusion coefficient, the
mass density contrast of the coexisting phases, and the viscosity of the bulk
phase. The agreement of observations and the prediction is demonstrated for
methanol/hexane and isobutoxyethanol/water mixtures where we determined \Delta
t for a vast range of ramp rates, \xi, and temperatures. The very good
quantitative agreement demonstrates that it is sufficient for binary mixtures
to consider (i) droplet growth by diffusive accretion that relaxes
supersaturation, and (ii) growth by collisions of sedimenting droplets. An
analytical solution of the resulting model provides a quantitative description
of the dependence of \Delta t on the ramp rate and the material constants.
Extensions of the model that will admit a quantitative prediction of \Delta t
in other settings are addressed. | cond-mat_stat-mech |
Two-bath model for activated surface diffusion of interacting adsorbates: The diffusion and low vibrational motions of adsorbates on surfaces can be
well described by a purely stochastic model, the so-called interacting single
adsorbate model, for low-moderate coverages (\theta \lesssim 0.12). Within this
model, the effects of thermal surface phonons and adsorbate-adsorbate
collisions are accounted for by two uncorrelated noise functions which arise in
a natural way from a two-bath model based on a generalization of the one-bath
Caldeira-Leggett Hamiltonian. As an illustration, the model is applied to the
diffusion of Na atoms on a Cu(001) surface with different coverages. | cond-mat_stat-mech |
Glassy dynamics: effective temperatures and intermittencies from a
two-state model: We show the existence of intermittent dynamics in one of the simplest model
of a glassy system: the two-state model, which has been used to explain the
origin of the violation of the fluctuation-dissipation theorem. The dynamics is
analyzed through a Langevin equation for the evolution of the state of the
system through its energy landscape. The results obtained concerning the
violation factor and the non-Gaussian nature of the fluctuations are in good
qualitative agreement with experiments measuring the effective temperature and
the voltage fluctuations in gels and in polymer glasses. The method proposed
can be useful to study the dynamics of other slow relaxation systems in which
non-Gaussian fluctuations have been observed. | cond-mat_stat-mech |
Minimal knotted polygons in cubic lattices: An implementation of BFACF-style algorithms on knotted polygons in the simple
cubic, face centered cubic and body centered cubic lattice is used to estimate
the statistics and writhe of minimal length knotted polygons in each of the
lattices. Data are collected and analysed on minimal length knotted polygons,
their entropy, and their lattice curvature and writhe. | cond-mat_stat-mech |
Comment on `Monte Carlo simulation study of the two-stage percolation
transition in enhanced binary trees': The enhanced binary tree (EBT) is a nontransitive graph which has two
percolation thresholds $p_{c1}$ and $p_{c2}$ with $p_{c1}<p_{c2}$. Our Monte
Carlo study implies that the second threshold $p_{c2}$ is significantly lower
than a recent claim by Nogawa and Hasegawa (J. Phys. A: Math. Theor. {\bf 42}
(2009) 145001). This means that $p_{c2}$ for the EBT does not obey the duality
relation for the thresholds of dual graphs $p_{c2}+\overline{p}_{c1}=1$ which
is a property of a transitive, nonamenable, planar graph with one end. As in
regular hyperbolic lattices, this relation instead becomes an inequality
$p_{c2}+\overline{p}_{c1}<1$. We also find that the critical behavior is well
described by the scaling form previously found for regular hyperbolic lattices. | cond-mat_stat-mech |
Most probable path of an active Brownian particle: In this study, we investigate the transition path of a free active Brownian
particle (ABP) on a two-dimensional plane between two given states. The
extremum conditions for the most probable path connecting the two states are
derived using the Onsager--Machlup integral and its variational principle. We
provide explicit solutions to these extremum conditions and demonstrate their
nonuniqueness through an analogy with the pendulum equation indicating possible
multiple paths. The pendulum analogy is also employed to characterize the shape
of the globally most probable path obtained by explicitly calculating the path
probability for multiple solutions. We comprehensively examine a translation
process of an ABP to the front as a prototypical example. Interestingly, the
numerical and theoretical analyses reveal that the shape of the most probable
path changes from an I to a U shape and to the $\ell$ shape with an increase in
the transition process time. The Langevin simulation also confirms this shape
transition. We also discuss further method applications for evaluating a
transition path in rare events in active matter. | cond-mat_stat-mech |
A Finite Temperature Treatment of Ultracold Atoms in a 1-D Optical
Lattice: We consider the effects of temperature upon the superfluid phase of
ultracold, weakly interacting bosons in a one dimensional optical lattice. We
use a finite temperature treatment of the Bose-Hubbard model based upon the
Hartree-Fock-Bogoliubov formalism, considering both a translationally invariant
lattice and one with additional harmonic confinement. In both cases we observe
an upward shift in the critical temperature for Bose condensation. For the case
with additional harmonic confinement, this is in contrast with results for the
uniform gas. | cond-mat_stat-mech |
Zero-temperature glass transition in two dimensions: The nature of the glass transition is theoretically understood in the
mean-field limit of infinite spatial dimensions, but the problem remains
totally open in physical dimensions. Nontrivial finite-dimensional fluctuations
are hard to control analytically, and experiments fail to provide conclusive
evidence regarding the nature of the glass transition. Here, we use Monte Carlo
simulations that fully bypass the glassy slowdown, and access equilibrium
states in two-dimensional glass-forming liquids at low enough temperatures to
directly probe the transition. We find that the liquid state terminates at a
thermodynamic glass transition at zero temperature, which is associated with an
entropy crisis and a diverging static correlation length. | cond-mat_stat-mech |
The Visibility Graphs of Correlated Time Series Violate the Barthelemy's
Conjecture for Degree and Betweenness Centralities: The problem of betweenness centrality remains a fundamental unsolved problem
in complex networks. After a pioneering work by Barthelemy, it has been
well-accepted that the maximal betweenness-degree ($b$-$k$) exponent for
scale-free (SF) networks is $\eta_{\text{max}}=2$, belonging to scale-free
trees (SFTs), based on which one concludes $\delta\ge\frac{\gamma+1}{2}$, where
$\gamma$ and $\delta$ are the scaling exponents of the distribution functions
of the degree and betweenness centrality, respectively. Here we present
evidence for violation of this conjecture for SF visibility graphs (VGs). To
this end, we consider the VG of three models: two-dimensional (2D)
Bak-Tang-Weisenfeld (BTW) sandpile model, 1D fractional Brownian motion (FBM)
and, 1D Levy walks, the two later cases are controlled by the Hurst exponent
$H$ and step-index $\alpha$, respectively. Specifically, for the BTW model and
FBM with $H\lesssim 0.5$, $\eta$ is greater than $2$, and also
$\delta<\frac{\gamma+1}{2}$ for the BTW model, while Barthelemy's conjecture
remains valid for the Levy process. We argue that this failure of Barthelemy's
conjecture is due to large fluctuations in the scaling $b$-$k$ relation
resulting in the violation of hyperscaling relation
$\eta=\frac{\gamma-1}{\delta-1}$ and emergent anomalous behaviors for the BTW
model and FBM. A super-universal behavior is found for the distribution
function for a generalized degree function identical to the Barabasi-Albert
network model. | cond-mat_stat-mech |
Symmetry enriched phases of quantum circuits: Quantum circuits consisting of random unitary gates and subject to local
measurements have been shown to undergo a phase transition, tuned by the rate
of measurement, from a state with volume-law entanglement to an area-law state.
From a broader perspective, these circuits generate a novel ensemble of quantum
many-body states at their output. In this paper, we characterize this ensemble
and classify the phases that can be established as steady states. Symmetry
plays a nonstandard role in that the physical symmetry imposed on the circuit
elements does not on its own dictate the possible phases. Instead, it is
extended by dynamical symmetries associated with this ensemble to form an
enlarged symmetry. Thus, we predict phases that have no equilibrium counterpart
and could not have been supported by the physical circuit symmetry alone. We
give the following examples. First, we classify the phases of a circuit
operating on qubit chains with $\mathbb{Z}_2$ symmetry. One striking
prediction, corroborated with numerical simulation, is the existence of
distinct volume-law phases in one dimension, which nonetheless support true
long-range order. We furthermore argue that owing to the enlarged symmetry,
this system can in principle support a topological area-law phase, protected by
the combination of the circuit symmetry and a dynamical permutation symmetry.
Second, we consider a Gaussian fermionic circuit that only conserves fermion
parity. Here the enlarged symmetry gives rise to a $U(1)$ critical phase at
moderate measurement rates and a Kosterlitz-Thouless transition to area-law
phases. We comment on the interpretation of the different phases in terms of
the capacity to encode quantum information. We discuss close analogies to the
theory of spin glasses pioneered by Edwards and Anderson as well as crucial
differences that stem from the quantum nature of the circuit ensemble. | cond-mat_stat-mech |
Statistics of quantum transmission in one dimension with broad disorder: We study the statistics of quantum transmission through a one-dimensional
disordered system modelled by a sequence of independent scattering units. Each
unit is characterized by its length and by its action, which is proportional to
the logarithm of the transmission probability through this unit. Unit actions
and lengths are independent random variables, with a common distribution that
is either narrow or broad. This investigation is motivated by results on
disordered systems with non-stationary random potentials whose fluctuations
grow with distance.
In the statistical ensemble at fixed total sample length four phases can be
distinguished, according to the values of the indices characterizing the
distribution of the unit actions and lengths. The sample action, which is
proportional to the logarithm of the conductance across the sample, is found to
obey a fluctuating scaling law, and therefore to be non-self-averaging, in
three of the four phases. According to the values of the two above mentioned
indices, the sample action may typically grow less rapidly than linearly with
the sample length (underlocalization), more rapidly than linearly
(superlocalization), or linearly but with non-trivial sample-to-sample
fluctuations (fluctuating localization). | cond-mat_stat-mech |
Competition between relaxation and external driving in the dissipative
Landau-Zener problem: We study Landau-Zener transitions in a dissipative environment by means of
the quasiadiabatic propagator path-integral scheme. It allows to obtain
numerically exact results for the full range of the involved parameters. We
discover a nonmonotonic dependence of the Landau-Zener transition probability
on the sweep velocity which is explained in terms of a simple physical picture.
This feature results from a nontrivial competition between relaxation processes
and the external sweep and is not captured by perturbative approaches. In
addition to the Landau-Zener transition probability, we study the excitation
survival probability and also provide a qualitative understanding of the
involved competition of time scales. | cond-mat_stat-mech |
Probabilistic analysis of the phase space flow for linear programming: The phase space flow of a dynamical system leading to the solution of Linear
Programming (LP) problems is explored as an example of complexity analysis in
an analog computation framework. An ensemble of LP problems with $n$ variables
and $m$ constraints ($n>m$), where all elements of the vectors and matrices are
normally distributed is studied. The convergence time of a flow to the fixed
point representing the optimal solution is computed. The cumulative
distribution ${\cal F}^{(n,m)}(\Delta)$ of the convergence rate $\Delta_{min}$
to this point is calculated analytically, in the asymptotic limit of large
$(n,m)$, in the framework of Random Matrix Theory. In this limit ${\cal
F}^{(n,m)}(\Delta)$ is found to be a scaling function, namely it is a function
of one variable that is a combination of $n$, $m$ and $\Delta$ rather then a
function of these three variables separately. From numerical simulations also
the distribution of the computation times is calculated and found to be a
scaling function as well. | cond-mat_stat-mech |
Farey Graphs as Models for Complex Networks: Farey sequences of irreducible fractions between 0 and 1 can be related to
graph constructions known as Farey graphs. These graphs were first introduced
by Matula and Kornerup in 1979 and further studied by Colbourn in 1982 and they
have many interesting properties: they are minimally 3-colorable, uniquely
Hamiltonian, maximally outerplanar and perfect. In this paper we introduce a
simple generation method for a Farey graph family, and we study analytically
relevant topological properties: order, size, degree distribution and
correlation, clustering, transitivity, diameter and average distance. We show
that the graphs are a good model for networks associated with some complex
systems. | cond-mat_stat-mech |
Real-Time Wavelet-transform spectrum analyzer for the investigation of
1/f^αnoise: A wavelet transform spectrum analyzer operating in real time within the
frequency range 3X10^(-5) - 1.3X10^5 Hz has been implemented on a low-cost
Digital Signal Processing board operating at 150MHz. The wavelet decomposition
of the signal allows to efficiently process non-stationary signals dominated by
large amplitude events fairly well localized in time, thus providing the
natural tool to analyze processes characterized by 1/f^alpha power spectrum.
The parallel architecture of the DSP allows the real-time processing of the
wavelet transform of the signal sampled at 0.3MHz. The bandwidth is about
220dB, almost ten decades. The power spectrum of the scattered intensity is
processed in real time from the mean square value of the wavelet coefficients
within each frequency band. The performances of the spectrum analyzer have been
investigated by performing Dynamic Light Scattering experiments on colloidal
suspensions and by comparing the measured spectra with the correlation
functions data obtained with a traditional multi tau correlator. In order to
asses the potentialities of the spectrum analyzer in the investigation of
processes involving a wide range of timescales, we have performed measurements
on a model system where fluctuations in the scattered intensities are generated
by the number fluctuations in a dilute colloidal suspension illuminated by a
wide beam. This system is characterized by a power-law spectrum with exponent
-3/2 in the scattered intensity fluctuations. The spectrum analyzer allows to
recover the power spectrum with a dynamic range spanning about 8 decades. The
advantages of wavelet analysis versus correlation analysis in the investigation
of processes characterized by a wide distribution of time scales and
non-stationary processes are briefly discussed. | cond-mat_stat-mech |
Onsager coefficients of a finite-time Carnot cycle: We study a finite-time Carnot cycle of a weakly interacting gas which we can
regard as a nearly ideal gas in the limit of $T_\mathrm{h}-T_\mathrm{c}\to 0$
where $T_\mathrm{h}$ and $T_\mathrm{c}$ are the temperatures of the hot and
cold heat reservoirs, respectively. In this limit, we can assume that the cycle
is working in the linear-response regime and can calculate the Onsager
coefficients of this cycle analytically using the elementary molecular kinetic
theory. We reveal that these Onsager coefficients satisfy the so-called
tight-coupling condition and this fact explains why the efficiency at the
maximal power $\eta_\mathrm{max}$ of this cycle can attain the Curzon-Ahlborn
efficiency from the viewpoint of the linear-response theory. | cond-mat_stat-mech |
Overdamped dynamics of particles with repulsive power-law interactions: We investigate the dynamics of overdamped $D$-dimensional systems of
particles repulsively interacting through short-ranged power-law potentials,
$V(r)\sim r^{-\lambda}\;(\lambda/D>1)$. We show that such systems obey a
non-linear diffusion equation, and that their stationary state extremizes a
$q$-generalized nonadditive entropy. Here we focus on the dynamical evolution
of these systems. Our first-principle $D=1,2$ many-body numerical simulations
(based on Newton's law) confirm the predictions obtained from the
time-dependent solution of the non-linear diffusion equation, and show that the
one-particle space-distribution $P(x,t)$ appears to follow a compact-support
$q$-Gaussian form, with $q=1-\lambda/D$. We also calculate the velocity
distributions $P(v_x,t)$ and, interestingly enough, they follow the same
$q$-Gaussian form (apparently precisely for $D=1$, and nearly so for $D=2$).
The satisfactory match between the continuum description and the molecular
dynamics simulations in a more general, time-dependent, framework neatly
confirms the idea that the present dissipative systems indeed represent
suitable applications of the $q$-generalized thermostatistical theory. | cond-mat_stat-mech |
Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein
condensates: We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas
coupled to a diatomic molecular Bose gas by coherent Raman transitions. This
system is shown to result in a new type of `superchemistry', in which giant
collective oscillations between the atomic and molecular gas can occur. The
phenomenon is caused by stimulated emission of bosonic atoms or molecules into
their condensate phases. | cond-mat_stat-mech |
Resilience of the topological phases to frustration: Recently it was highlighted that one-dimensional antiferromagnetic spin
models with frustrated boundary conditions, i.e. periodic boundary conditions
in a ring with an odd number of elements, may show very peculiar behavior.
Indeed the presence of frustrated boundary conditions can destroy the local
magnetic orders presented by the models when different boundary conditions are
taken into account and induce novel phase transitions. Motivated by these
results, we analyze the effects of the introduction of frustrated boundary
conditions on several models supporting (symmetry protected) topological
orders, and compare our results with the ones obtained with different boundary
conditions. None of the topological order phases analyzed are altered by this
change. This observation leads naturally to the conjecture that topological
phases of one-dimensional systems are in general not affected by topological
frustration. | cond-mat_stat-mech |
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