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Reaction-diffusion processes and metapopulation models in heterogeneous
networks: Dynamical reaction-diffusion processes and meta-population models are
standard modeling approaches for a wide variety of phenomena in which local
quantities - such as density, potential and particles - diffuse and interact
according to the physical laws. Here, we study the behavior of two basic
reaction-diffusion processes ($B \to A$ and $A+B \to 2B$) defined on networks
with heterogeneous topology and no limit on the nodes' occupation number. We
investigate the effect of network topology on the basic properties of the
system's phase diagram and find that the network heterogeneity sustains the
reaction activity even in the limit of a vanishing density of particles,
eventually suppressing the critical point in density driven phase transitions,
whereas phase transition and critical points, independent of the particle
density, are not altered by topological fluctuations. This work lays out a
theoretical and computational microscopic framework for the study of a wide
range of realistic meta-populations models and agent-based models that include
the complex features of real world networks. | cond-mat_stat-mech |
Many-body Localization with Dipoles: Systems of strongly interacting dipoles offer an attractive platform to study
many-body localized phases, owing to their long coherence times and strong
interactions. We explore conditions under which such localized phases persist
in the presence of power-law interactions and supplement our analytic treatment
with numerical evidence of localized states in one dimension. We propose and
analyze several experimental systems that can be used to observe and probe such
states, including ultracold polar molecules and solid-state magnetic spin
impurities. | cond-mat_stat-mech |
Financial Modeling and Option Theory with the Truncated Levy Process: In recent studies the truncated Levy process (TLP) has been shown to be very
promising for the modeling of financial dynamics. In contrast to the Levy
process, the TLP has finite moments and can account for both the previously
observed excess kurtosis at short timescales, along with the slow convergence
to Gaussian at longer timescales. I further test the truncated Levy paradigm
using high frequency data from the Australian All Ordinaries share market
index. I then consider, for the early Levy dominated regime, the issue of
option hedging for two different hedging strategies that are in some sense
optimal. These are compared with the usual delta hedging approach and found to
differ significantly. I also derive the natural generalization of the
Black-Scholes option pricing formula when the underlying security is modeled by
a geometric TLP. This generalization would not be possible without the
truncation. | cond-mat_stat-mech |
Thermodynamics of feedback controlled systems: We compute the entropy reduction in feedback controlled systems due to the
repeated operation of the controller. This was the lacking ingredient to
establish the thermodynamics of these systems, and in particular of Maxwell's
demons. We illustrate some of the consequences of our general results by
deriving the maximum work that can be extracted from isothermal feedback
controlled systems. As a case example, we finally study a simple system that
performs an isothermal information-fueled particle pumping. | cond-mat_stat-mech |
Dynamics and correlations in Motzkin and Fredkin spin chains: The Motzkin and Fredkin quantum spin chains are described by frustration-free
Hamiltonians recently introduced and studied because of their anomalous
behaviors in the correlation functions and in the entanglement properties. In
this paper we analyze their quantum dynamical properties, focusing in
particular on the time evolution of the excitations driven by a quantum quench,
looking at the correlations functions of spin operators defined along different
directions, and discussing the results in relation with the cluster
decomposition property. | cond-mat_stat-mech |
Interevent time distribution, burst, and hybrid percolation transition: Critical phenomena of a second-order percolation transition are known to be
independent of cluster merging or pruning process. However, those of a hybrid
percolation transition (HPT), mixed properties of both first-order and
second-order transitions, depend on the processes. The HPT induced by cluster
merging is more intrigue and little understood than the other. Here, we
construct a theoretical framework using the so-called restricted percolation
model. In this model, clusters are ranked by size and partitioned into small-
and large-cluster sets. As the cluster rankings are updated by cluster
coalescence, clusters may move back and forth across the set boundary. The
inter-event time (IET) between two consecutive crossing times have two
distributions with power-law decays, which in turn characterize the criticality
of the HPT. A burst of such crossing events occurs and signals the upcoming
transition. We discuss a related phenomenon to this critical dynamics. | cond-mat_stat-mech |
A new effective-field technique for the ferromagnetic spin-1 Blume-Capel
model in a transverse crystal field: A new approximating technique is developed so as to study the quantum
ferromagnetic spin-1 Blume-Capel model in the presence of a transverse crystal
field in the square lattice. Our proposal consists of approaching the spin
system by considering islands of finite clusters whose frontiers are surrounded
by non-interacting spins that are treated by the effective-field theory. The
resulting phase diagram is qualitatively correct, in contrast to most
effective-field treatments, in which the first-order line exhibits spurious
behavior by not being perpendicular to the anisotropy axis at low temperatures.
The effect of the transverse anisotropy is also verified by the presence of
quantum phase transitions. The possibility of using larger sizes constitutes an
advantage to other approaches where the implementation of larger sizes is
costly computationally. | cond-mat_stat-mech |
From Linear to Nonlinear Responses of Thermal Pure Quantum States: We propose a self-validating scheme to calculate the unbiased responses of
quantum many-body systems to external fields of arbibraty strength at any
temperature. By switching on a specified field to a thermal pure quantum state
of an isolated system, and tracking its time evolution, one can observe an
intrinsic thermalization process driven solely by many-body effects. The
transient behavior before thermalization contains rich information on excited
states, giving the linear and nonlinear response functions at all frequencies.
We uncover the necessary conditions to clarify the applicability of this
formalism, supported by a proper definition of the nonlinear response function.
The accuracy of the protocol is guaranteed by a rigorous upper bound of error
exponentially decreasing with system size, and is well implemented in the
simple ferromagnetic Heisenberg chain, whose response at high fields exhibits a
nonlinear band deformation. We further extract the characteristic features of
excitation of the spin-1/2 kagome antiferromagnet; the wavenumber-insensitive
linear responses from the possible spin liquid ground state, and the
significantly broad nonlinear peaks which should be generated from numerous
collisions of quasi-particles, that are beyond the perturbative description. | cond-mat_stat-mech |
Evaluating the RiskMetrics Methodology in Measuring Volatility and
Value-at-Risk in Financial Markets: We analyze the performance of RiskMetrics, a widely used methodology for
measuring market risk. Based on the assumption of normally distributed returns,
the RiskMetrics model completely ignores the presence of fat tails in the
distribution function, which is an important feature of financial data.
Nevertheless, it was commonly found that RiskMetrics performs satisfactorily
well, and therefore the technique has become widely used in the financial
industry. We find, however, that the success of RiskMetrics is the artifact of
the choice of the risk measure. First, the outstanding performance of
volatility estimates is basically due to the choice of a very short (one-period
ahead) forecasting horizon. Second, the satisfactory performance in obtaining
Value-at-Risk by simply multiplying volatility with a constant factor is mainly
due to the choice of the particular significance level. | cond-mat_stat-mech |
q-Gaussians in the porous-medium equation: stability and time evolution: The stability of $q$-Gaussian distributions as particular solutions of the
linear diffusion equation and its generalized nonlinear form,
$\pderiv{P(x,t)}{t} = D \pderiv{^2 [P(x,t)]^{2-q}}{x^2}$, the
\emph{porous-medium equation}, is investigated through both numerical and
analytical approaches. It is shown that an \emph{initial} $q$-Gaussian,
characterized by an index $q_i$, approaches the \emph{final}, asymptotic
solution, characterized by an index $q$, in such a way that the relaxation rule
for the kurtosis evolves in time according to a $q$-exponential, with a
\emph{relaxation} index $q_{\rm rel} \equiv q_{\rm rel}(q)$. In some cases,
particularly when one attempts to transform an infinite-variance distribution
($q_i \ge 5/3$) into a finite-variance one ($q<5/3$), the relaxation towards
the asymptotic solution may occur very slowly in time. This fact might shed
some light on the slow relaxation, for some long-range-interacting many-body
Hamiltonian systems, from long-standing quasi-stationary states to the ultimate
thermal equilibrium state. | cond-mat_stat-mech |
Nonlinear transport in inelastic Maxwell mixtures under simple shear
flow: The Boltzmann equation for inelastic Maxwell models is used to analyze
nonlinear transport in a granular binary mixture in the steady simple shear
flow. Two different transport processes are studied. First, the rheological
properties (shear and normal stresses) are obtained by solving exactly the
velocity moment equations. Second, the diffusion tensor of impurities immersed
in a sheared inelastic Maxwell gas is explicitly determined from a perturbation
solution through first order in the concentration gradient. The corresponding
reference state of this expansion corresponds to the solution derived in the
(pure) shear flow problem. All these transport coefficients are given in terms
of the restitution coefficients and the parameters of the mixture (ratios of
masses, concentration, and sizes). The results are compared with those obtained
analytically for inelastic hard spheres in the first Sonine approximation and
by means of Monte Carlo simulations. The comparison between the results
obtained for both interaction models shows a good agreement over a wide range
values of the parameter space. | cond-mat_stat-mech |
Bose-Einstein Condensation, the Lambda Transition, and Superfluidity for
Interacting Bosons: Bose-Einstein condensation and the $\lambda$-transition are described in
molecular detail for bosons interacting with a pair potential. New phenomena
are identified that are absent in the usual ideal gas treatment. Monte Carlo
simulations of Lennard-Jones helium-4 neglecting ground momentum state bosons
give a diverging heat capacity approaching the transition. Pure permutation
loops give continuous growth in the occupancy of the ground momentum state.
Mixed ground and excited momentum state permutation loops give a discontinuous
transition to the condensed phase. The consequent latent heat for the
$\lambda$-transition is 3\% of the total energy. The predicted critical
velocity for superfluid flow is within a factor of three of the measured values
over three orders of magnitude in pore diameter. | cond-mat_stat-mech |
Refrustration and competing orders in the prototypical Dy2Ti2O7 spin ice
material: Spin ices, frustrated magnetic materials analogous to common water ice, are
exemplars of high frustration in three dimensions. Recent experimental studies
of the low-temperature properties of the paradigmatic Dy$_2$Ti$_2$O$_7$ spin
ice material, in particular whether the predicted transition to long-range
order occurs, raise questions as per the currently accepted microscopic model
of this system. In this work, we combine Monte Carlo simulations and mean-field
theory calculations to analyze data from magnetization, elastic neutron
scattering and specific heat measurements on Dy$_2$Ti$_2$O$_7$. We also
reconsider the possible importance of the nuclear specific heat, $C_{\rm nuc}$,
in Dy$_2$Ti$_2$O$_7$. We find that $C_{\rm nuc}$ is not entirely negligible
below a temperature $\sim 0.5$ K and must be taken into account in a
quantitative analysis of the calorimetric data of this compound below that
temperature. We find that small effective exchange interactions compete with
the magnetostatic dipolar interaction responsible for the main spin ice
phenomenology. This causes an unexpected "refrustration" of the long-range
order that would be expected from the incompletely self-screened dipolar
interaction and which positions the material at the boundary between two
competing classical long-range ordered ground states. This allows for the
manifestation of new physical low-temperature phenomena in Dy$_2$Ti$_2$O$_7$,
as exposed by recent specific heat measurements. We show that among the four
most likely causes for the observed upturn of the specific heat at low
temperature -- an exchange-induced transition to long-range order, quantum
non-Ising (transverse) terms in the effective spin Hamiltonian, the nuclear
hyperfine contribution and random disorder -- only the last appears to be
reasonably able to explain the calorimetric data. | cond-mat_stat-mech |
Scaling functions and amplitude ratios for the Potts model on an
uncorrelated scale-free network: We study the critical behaviour of the $q$-state Potts model on an
uncorrelated scale-free network having a power-law node degree distribution
with a decay exponent $\lambda$. Previous data show that the phase diagram of
the model in the $q,\lambda$ plane in the second order phase transition regime
contains three regions, each being characterized by a different set of critical
exponents. In this paper we complete these results by finding analytic
expressions for the scaling functions and critical amplitude ratios in the
above mentioned regions. Similar to the previously found critical exponents,
the scaling functions and amplitude ratios appear to be $\lambda$-dependent. In
this way, we give a comprehensive description of the critical behaviour in a
new universality class. | cond-mat_stat-mech |
A Fluid Dynamic Model for the Movement of Pedestrians: A kind of fluid dynamic description for the collective movement of
pedestrians is developed on the basis of a Boltzmann-like gaskinetic model. The
differences between these pedestrian specific equations and those for ordinary
fluids are worked out, for example concerning the mechanism of relaxation to
equilibrium, the role of ``pressure'', the special influence of internal
friction and the origin of ``temperature''. Some interesting results are
derived that can be compared to real situations, for example the development of
walking lanes and of pedestrian jams, the propagation of waves, and the
behavior on a dance floor. Possible applications of the model to town- and
traffic-planning are outlined. | cond-mat_stat-mech |
Synchronization and directed percolation in coupled map lattices: We study a synchronization mechanism, based on one-way coupling of
all-or-nothing type, applied to coupled map lattices with several different
local rules. By analyzing the metric and the topological distance between the
two systems, we found two different regimes: a strong chaos phase in which the
transition has a directed percolation character and a weak chaos phase in which
the synchronization transition occurs abruptly. We are able to derive some
analytical approximations for the location of the transition point and the
critical properties of the system.
We propose to use the characteristics of this transition as indicators of the
spatial propagation of chaoticity. | cond-mat_stat-mech |
Effects of the randomly distributed magnetic field on the phase diagrams
of the transverse Ising thin film: The effect of the zero centered Gaussian random magnetic field distribution
on the phase diagrams and ground state magnetizations of the transverse Ising
thin film has been investigated. As a formulation, the differential operator
technique and decoupling approximation within the effective field theory has
been used. The variation of the phase diagrams with the Gaussian distribution
width (\sigma) has been obtained and particular attention has been paid on the
evolution of the special point coordinate with distribution parameter. In
addition, the ground state longitudinal and transverse magnetization behaviors
have been investigated in detail. | cond-mat_stat-mech |
Phase separation in a wedge. Exact results: The exact theory of phase separation in a two-dimensional wedge is derived
from the properties of the order parameter and boundary condition changing
operators in field theory. For a shallow wedge we determine the passage
probability for an interface with endpoints on the boundary. For generic
opening angles we exhibit the fundamental origin of the filling transition
condition and of the property known as wedge covariance. | cond-mat_stat-mech |
Phase separation in fluids exposed to spatially periodic external fields: We consider the liquid-vapor type phase transition for fluids confined within
spatially periodic external fields. For a fluid in d=3 dimensions, the periodic
field induces an additional phase, characterized by large density modulations
along the field direction. At the triple point, all three phases (modulated,
vapor, and liquid) coexist. At temperatures slightly above the triple point and
for low (high) values of the chemical potential, two-phase coexistence between
the modulated phase and the vapor (liquid) is observed. We study this
phenomenon using computer simulations and mean-field theory for the Ising
model. The theory shows that, in order for the modulated phase to arise, the
field wavelength must exceed a threshold value. We also find an extremely low
tension of the interface between the modulated phase and the vapor/liquid
phases. The tension is of the order 10^{-4} kB T per squared lattice spacing,
where kB is the Boltzmann constant, and T the temperature. In order to detect
such low tensions, a new simulation method is proposed. We also consider the
case of d=2 dimensions. The modulated phase then does not survive, leading to a
radically different phase diagram. | cond-mat_stat-mech |
An extended scaling analysis of the S=1/2 Ising ferromagnet on the
simple cubic lattice: It is often assumed that for treating numerical (or experimental) data on
continuous transitions the formal analysis derived from the Renormalization
Group Theory can only be applied over a narrow temperature range, the "critical
region"; outside this region correction terms proliferate rendering attempts to
apply the formalism hopeless. This pessimistic conclusion follows largely from
a choice of scaling variables and scaling expressions which is traditional but
which is very inefficient for data covering wide temperature ranges. An
alternative "extended caling" approach can be made where the choice of scaling
variables and scaling expressions is rationalized in the light of well
established high temperature series expansion developments. We present the
extended scaling approach in detail, and outline the numerical technique used
to study the 3d Ising model. After a discussion of the exact expressions for
the historic 1d Ising spin chain model as an illustration, an exhaustive
analysis of high quality numerical data on the canonical simple cubic lattice
3d Ising model is given. It is shown that in both models, with appropriate
scaling variables and scaling expressions (in which leading correction terms
are taken into account where necessary), critical behavior extends from Tc up
to infinite temperature. | cond-mat_stat-mech |
Jamming vs. Caging in Three Dimensional Jamming Percolation: We investigate a three-dimensional kinetically-constrained model that
exhibits two types of phase transitions at different densities. At the jamming
density $ \rho_J $ there is a mixed-order phase transition in which a finite
fraction of the particles become frozen, but the other particles may still
diffuse throughout the system. At the caging density $ \rho_C > \rho_J $, the
mobile particles are trapped in finite cages and no longer diffuse. The caging
transition occurs due to a percolation transition of the unfrozen sites, and we
numerically find that it is a continuous transition with the same critical
exponents as random percolation. | cond-mat_stat-mech |
Landauer's erasure principle in non-equilibrium systems: In two recent papers, Maroney and Turgut separately and independently show
generalisations of Landauer's erasure principle to indeterministic logical
operations, as well as to logical states with variable energies and entropies.
Here we show that, although Turgut's generalisation seems more powerful, in
that it implies but is not implied by Maroney's and that it does not rely upon
initial probability distributions over logical states, it does not hold for
non-equilibrium states, while Maroney's generalisation holds even in
non-equilibrium. While a generalisation of Turgut's inequality to
non-equilibrium seems possible, it lacks the properties that makes the
equilibrium inequality appealing. The non-equilibrium generalisation also no
longer implies Maroney's inequality, which may still be derived independently.
Furthermore, we show that Turgut's inequality can only give a necessary, but
not sufficient, criteria for thermodynamic reversibility. Maroney's inequality
gives the necessary and sufficient conditions. | cond-mat_stat-mech |
Stochastic PDEs: domain formation in dynamic transitions: Spatiotemporal evolution in the real Ginzburg-Landau equation is studied with
space-time noise and a slowly increasing critical parameter. Analytical
estimates for the characteristic size of the domains formed in a slow sweep
through the critical point agree with the results of finite difference solution
of the stochastic PDEs. | cond-mat_stat-mech |
Three lemmas on the dynamic cavity method: We study the dynamic cavity method for dilute kinetic Ising models with
synchronous update rules. For the parallel update rule we find for fully
asymmetric models that the dynamic cavity equations reduce to a Markovian
dynamics of the (time-dependent) marginal probabilities. For the random
sequential update rule, also an instantiation of a synchronous update rule, we
find on the other hand that the dynamic cavity equations do not reduce to a
Markovian dynamics, unless an additional assumption of time factorization is
introduced. For symmetric models we show that a fixed point of ordinary Belief
propagation is also a fixed point of the dynamic cavity equations in the time
factorized approximation. For clarity, the conclusions of the paper are
formulated as three lemmas. | cond-mat_stat-mech |
Exactly solvable model of stochastic heat engine: Optimization of power,
its fluctuations and efficiency: We investigate a stochastic heat engine based on an over-damped particle
diffusing on the positive real axis in an externally driven time-periodic
log-harmonic potential. The periodic driving is composed of two isothermal and
two adiabatic branches. Within our specific setting we verify the recent
universal results regarding efficiency at maximum power and discuss properties
of the optimal protocol. Namely, we show that for certain fixed parameters the
optimal protocol maximizes not only the output power but also the efficiency.
Moreover, we calculate the variance of the output work and discuss the
possibility to minimize fluctuations of the output power. | cond-mat_stat-mech |
Transport coefficients for hard-sphere relativistic gas: Transport coefficients are of crucial importance in theoretical as well as
experimental studies. Despite substantial research on classical hard
sphere/disk gases in low and high density regimes, a thorough investigation of
transport coefficients for massive relativistic systems is missing in the
literature. In this work a fully relativistic molecular dynamics simulation is
employed to numerically obtain the transport coefficients of a hard sphere
relativistic gas based on Helfand-Einstein expressions. The numerical data are
then used to check the accuracy of Chapmann-Enskog (CE) predictions in a wide
range of temperature. The results indicate that while simulation data in low
temperature regime agrees very well with theoretical predictions, it begins to
show deviations as temperature rises, except for the thermal conductivity which
fits very well to CE theory in the whole range of temperature. Since our
simulations are done in low density regimes, where CE approximation is expected
to be valid, the observed deviations can be attributed to the inaccuracy of
linear CE theory in extremely relativistic cases. | cond-mat_stat-mech |
Extended loop algorithm for pyrochlore Heisenberg spin models with
spin-ice type degeneracy: application to spin-glass transition in
antiferromagnets coupled to local lattice distortions: For Ising spin models which bear the spin-ice type macroscopic
(quasi-)degeneracy, conventional classical Monte Carlo (MC) simulation using
single spin flips suffers from dynamical freezing at low temperatures ($T$). A
similar difficulty is seen also in a family of Heisenberg spin models with
easy-axis anisotropy or biquadratic interactions. In the Ising case, the
difficulty is avoided by introducing a non-local update based on the loop
algorithm. We present an extension of the loop algorithm to the Heisenberg
case. As an example of its application, we review our recent study on
spin-glass (SG) transition in a bond-disordered Heisenberg antiferromagnet
coupled to local lattice distortions. | cond-mat_stat-mech |
Towards lattice-gas description of low-temperature properties above the
Haldane and cluster-based Haldane ground states of a mixed spin-(1,1/2)
Heisenberg octahedral chain: The rich ground-state phase diagram of the mixed spin-(1,1/2) Heisenberg
octahedral chain was previously elaborated from effective mixed-spin Heisenberg
chains, which were derived by employing a local conservation of a total spin on
square plaquettes of an octahedral chain. Here we present a comprehensive
analysis of the thermodynamic properties of this model. In the highly
frustrated parameter region the lowest-energy eigenstates of the mixed-spin
Heisenberg octahedral chain belong to flat bands, which allow a precise
description of low-temperature magnetic properties within the localized-magnon
approach exploiting a classical lattice-gas model of hard-core monomers. The
present article provides a more comprehensive version of the localized-magnon
approach, which extends the range of its validity down to a less frustrated
parameter region involving the Haldane and cluster-based Haldane ground states.
A comparison between results of the developed localized-magnon theory and
accurate numerical methods such as full exact diagonalization and
finite-temperature Lanczos technique convincingly evidence that the
low-temperature magnetic properties above the Haldane and the cluster-based
Haldane ground states can be extracted from a classical lattice-gas model of
hard-core monomers and dimers, which is additionally supplemented by a
hard-core particle spanned over the whole lattice representing the gapped
Haldane phase. | cond-mat_stat-mech |
Precision-dissipation trade-off for driven stochastic systems: In this paper, I derive a closed expression for how precisely a small-scaled
system can follow a pre-defined trajectory, while keeping its dissipation below
a fixed limit. The total amount of dissipation is approximately inversely
proportional to the expected deviation from the pre-defined trajectory. The
optimal driving protocol is derived and it is shown that associated
time-dependent probability distribution conserves its shape throughout the
protocol. Potential applications are discussed in the context of bit erasure
and electronic circuits. | cond-mat_stat-mech |
On the CFT describing the spin clusters in 2d Potts model: We have considered clusters of like spin in the Q-Potts model, the spin Potts
clusters. Using Monte Carlo simulations, we studied these clusters on a square
lattice with periodic boundary conditions for values of Q in [1,4]. We continue
the work initiated with Delfino and Viti (2013) by measuring the universal
finite size corrections of the two-point connectivity. The numerical data are
perfectly compatible with the CFT prediction, thus supporting the existence of
a consistent CFT, still unknown, describing the connectivity Potts spin
clusters. We provided in particular new insights on the energy field of such
theory. For Q=2, we found a good agreement with the prediction that the Ising
spin clusters behave as the Fortuin-Kasteleyn ones at the tri-critical point of
the dilute 1-Potts model. We show that the structure constants are likely to be
given by the imaginary Liouville structure constants, consistently with the
results of Delfino et al. (2013) and of Ang and Sun (2021). For Q different
from 2 instead, the structure constants we measure do not correspond to any
known bootstrap solutions. The validity of our analysis is backed up by the
measures of the spin Potts clusters wrapping probability for Q=3. We evaluate
the main critical exponents and the correction to the scaling. A new exact and
compact expression for the torus one-point of the Q-Potts energy field is also
given. | cond-mat_stat-mech |
Fidelity susceptibility of the quantum Ising model in the transverse
field: The exact solution: We derive an exact closed-form expression for fidelity susceptibility of the
quantum Ising model in the transverse field. We also establish an exact
one-to-one correspondence between fidelity susceptibility in the ferromagnetic
and paramagnetic phases of this model. Elegant summation formulas are obtained
as a by-product of these studies. | cond-mat_stat-mech |
Breaking of scale invariance in the time dependence of correlation
functions in isotropic and homogeneous turbulence: In this paper, we present theoretical results on the statistical properties
of stationary, homogeneous and isotropic turbulence in incompressible flows in
three dimensions. Within the framework of the Non-Perturbative Renormalization
Group, we derive a closed renormalization flow equation for a generic $n$-point
correlation (and response) function for large wave-numbers with respect to the
inverse integral scale. The closure is obtained from a controlled expansion and
relies on extended symmetries of the Navier-Stokes field theory. It yields the
exact leading behavior of the flow equation at large wave-numbers $|\vec p_i|$,
and for arbitrary time differences $t_i$ in the stationary state. Furthermore,
we obtain the form of the general solution of the corresponding fixed point
equation, which yields the analytical form of the leading wave-number and time
dependence of $n$-point correlation functions, for large wave-numbers and both
for small $t_i$ and in the limit $t_i\to \infty$. At small $t_i$, the leading
contribution at large wave-number is logarithmically equivalent to $-\alpha
(\epsilon L)^{2/3}|\sum t_i \vec p_i|^2$, where $\alpha$ is a nonuniversal
constant, $L$ the integral scale and $\varepsilon$ the mean energy injection
rate. For the 2-point function, the $(t p)^2$ dependence is known to originate
from the sweeping effect. The derived formula embodies the generalization of
the effect of sweeping to $n-$point correlation functions. At large wave-number
and large $t_i$, we show that the $t_i^2$ dependence in the leading order
contribution crosses over to a $|t_i|$ dependence. The expression of the
correlation functions in this regime was not derived before, even for the
2-point function. Both predictions can be tested in direct numerical
simulations and in experiments. | cond-mat_stat-mech |
Metastable states in the FPU system: In this letter we report numerical results giving, as a function of time, the
energy fluctuation of a Fermi-Pasta-Ulam system in dynamical contact with a
heat bath, the initial data of the FPU system being extracted from a Gibbs
distribution at the same temperature of the bath. The aim is to get information
on the specific heat of the FPU system in the spirit of the
fluctuation--dissipation theorem. While the standard equilibrium result is
recovered at high temperatures, there exists a critical temperature below which
the energy fluctuation as a function of time tends to an asymptotic value
sensibly lower than the one expected at equilibrium. This fact appears to
exhibit the existence of a metastable state for generic initial conditions. An
analogous phenomenon of metastability was up to now observed in FPU systems
only for exceptional initial data having vanishing Gibbs measure, namely
excitations of a few low--frequency modes (as in the original FPU work). | cond-mat_stat-mech |
One-dimensional Superdiffusive Heat Propagation Induced by Optical
Phonon-Phonon Interactions: It is known that one-dimensional anomalous heat propagation is usually
characterized by a L\'{e}vy walk superdiffusive spreading function with two
side peaks located on the fronts due to the finite velocity of acoustic
phonons, and in the case when the acoustic phonons vanish, e.g., due to the
phonon-lattice interactions such that the system's momentum is not conserved,
the side peaks will disappear and a normal Gaussian diffusive heat propagating
behavior will be observed. Here we show that there exists another type of
superdiffusive, non-Gaussian heat propagation but without side peaks in a
typical nonacoustic, momentum-nonconserving system. It implies that thermal
transport in this system disobeys the Fourier law, in clear contrast with the
existing theoretical predictions. The underlying mechanism is related to a
novel effect of optical phonon-phonon interactions. These findings may open a
new avenue for further exploring thermal transport in low dimensions. | cond-mat_stat-mech |
Two-stage random sequential adsorption of discorectangles and disks on a
two-dimensional surface: The different variants of two-stage random sequential adsorption (RSA) models
for packing of disks and discorectangles on a two-dimensional (2D) surface were
investigated. In the SD model, the discorectangles were first deposited and
then the disks were added. In the DS model, the disks were first deposited and
then discorectangles were added. At the first stage the particles were
deposited up to the selected concentration and at the final (second) stage the
particles were deposited up to the saturated (jamming) state. The main
parameters of the models were the concentration of particles deposited at the
first stage, aspect ratio of the discorectangles $\varepsilon$ (length to
diameter of ratio $\varepsilon=l/d$) and disk diameter $D$. All distances were
measured using the value of $d$ as a unit of measurement of linear dimensions,
the disk diameter was varied in the interval $D \in [1-10]$, and the aspect
ratio value was varied in the interval $\varepsilon\in [1-50]$. The
dependencies of the jamming coverage of particles deposited at the second stage
versus the parameters of the models were analyzed. The presence of first
deposited particles for both models regulated the maximum possible disk
diameter, $D_{max}$ (SD model) or the maximum aspect ratio, $\varepsilon_{max}$
(DS model). This behavior was explained by the deposition of particles in the
second stage into triangular (SD model) or elongated (DS model) pores formed by
particles deposited at the first stage. The percolation connectivity of disks
(SD model) and discorectangles (DS model) for the particles with a hard core
and a soft shell structure was analyzed. The disconnectedness was ensured by
overlapping of soft shells. The dependencies of connectivity versus the
parameters of SD and DS models were also analyzed. | cond-mat_stat-mech |
Ergodicity of non-Hamiltonian equilibrium systems: It is well known that ergodic theory can be used to formally prove a weak
form of relaxation to equilibrium for finite, mixing, Hamiltonian systems. In
this Letter we extend this proof to any dynamics that preserves a mixing
equilibrium distribution. The proof uses an approach similar to that used in
umbrella sampling, and demonstrates the need for a form of ergodic consistency
of the initial and final distribution. This weak relaxation only applies to
averages of physical properties. It says nothing about whether the distribution
of states relaxes towards the equilibrium distribution or how long the
relaxation of physical averages takes. | cond-mat_stat-mech |
Self-tuning of threshold for a two-state system: A two-state system (TSS) under time-periodic perturbations (to be regarded as
input signals) is studied in connection with self-tuning (ST) of threshold and
stochastic resonance (SR). By ST, we observe the improvement of signal-to-noise
ratio (SNR) in a weak noise region. Analytic approach to a tuning equation
reveals that SNR improvement is possible also for a large noise region and this
is demonstrated by Monte Carlo simulations of hopping processes in a TSS. ST
and SR are discussed from a little more physical point of energy transfer
(dissipation) rate, which behaves in a similar way as SNR. Finally ST is
considered briefly for a double-well potential system (DWPS), which is closely
related to the TSS. | cond-mat_stat-mech |
Frustration of signed networks: How does it affect the thermodynamic
properties of a system?: Signed networks with positive and negative interaction are widely observed in
the real systems. The negative links would induce frustration, then affect
global properties of the system. Based on previous studies, frustration of
signed networks is investigated and quantified. Frustrations of $\pm J$
(Edwards-Anderson) Ising model with a concentration $p$ of negative bonds,
constructed on different networks, such as triangular lattice, square lattice
and random regular networks (RRN) with connectivity $k=6$ are estimated by
theoretical and numerical approaches. Based on the quantitative measurement of
frustration, its effects on phase transitions characterized by order parameter
$q_{EA}$ are studied. The relationship of critical temperature $T_c$ with the
quantified frustration $\mu$ is given by mean-field theory. It shows that $T_c$
decreases linearly with frustration $\mu$ . The theory is checked by numerical
estimations, such as the Metropolis algorithm and Replica Symmetric Population
Dynamics Algorithm. The numerical estimates are consistent well with the
mean-field prediction. | cond-mat_stat-mech |
Symmetry Hierarchy and Thermalization Frustration in Graphene
Nanoresonators: As the essential cause of the intrinsic dissipation that limits the quality
of graphene nanoresonators, intermodal energy transfer is also a key issue in
thermalization dynamics. Typically systems with larger initial energy demand
shorter time to be thermalized. However, we find quantitatively that instead of
becoming shorter, the equipartition time of the graphene nanoresonator can
increase abruptly by one order of magnitude. This thermalization frustration
emerges due to the partition of the normal modes based on the hierarchical
symmetry, and a sensitive on-off switching of the energy flow channels between
symmetry classes controlled by Mathieu instabilities. The results uncover the
decisive roles of symmetry in the thermalization at the nanoscale, and may also
lead to strategies for improving the performance of graphene nanoresonators. | cond-mat_stat-mech |
Dissipation, interaction and relative entropy: Many thermodynamic relations involve inequalities, with equality if a process
does not involve dissipation. In this article we provide equalities in which
the dissipative contribution is shown to involve the relative entropy (a.k.a.
Kullback-Leibler divergence). The processes considered are general time
evolutions both in classical and quantum mechanics, and the initial state is
sometimes thermal, sometimes partially so. As an application, the relative
entropy is related to transport coefficients. | cond-mat_stat-mech |
Extended-range percolation in complex networks: Classical percolation theory underlies many processes of information transfer
along the links of a network. In these standard situations, the requirement for
two nodes to be able to communicate is the presence of at least one
uninterrupted path of nodes between them. In a variety of more recent data
transmission protocols, such as the communication of noisy data via
error-correcting repeaters, both in classical and quantum networks, the
requirement of an uninterrupted path is too strict: two nodes may be able to
communicate even if all paths between them have interruptions/gaps consisting
of nodes that may corrupt the message. In such a case a different approach is
needed. We develop the theoretical framework for extended-range percolation in
networks, describing the fundamental connectivity properties relevant to such
models of information transfer. We obtain exact results, for any range $R$, for
infinite random uncorrelated networks and we provide a message-passing
formulation that works well in sparse real-world networks. The interplay of the
extended range and heterogeneity leads to novel critical behavior in scale-free
networks. | cond-mat_stat-mech |
Counterintuitive effect of gravity on the heat capacity of a metal
sphere: re-examination of a well-known problem: A well-known high-school problem asking the final temperature of two spheres
that are given the same amount of heat, one lying on a table and the other
hanging from a thread, is re-examined. The conventional solution states that
the sphere on the table ends up colder, since thermal expansion raises its
center of mass. It is found that this solution violates the second law of
thermodynamics and is therefore incorrect. Two different new solutions are
proposed. The first uses statistical mechanics, while the second is based on
purely classical thermodynamical arguments. It is found that gravity produces a
counterintuitive effect on the heat capacity, and the new answer to the problem
goes in the opposite direction of what traditionally thought. | cond-mat_stat-mech |
Optimal traffic organisation in ants under crowded conditions: Efficient transportation, a hot topic in nonlinear science, is essential for
modern societies and the survival of biological species. Biological evolution
has generated a rich variety of successful solutions, which have inspired
engineers to design optimized artificial systems. Foraging ants, for example,
form attractive trails that support the exploitation of initially unknown food
sources in almost the minimum possible time. However, can this strategy cope
with bottleneck situations, when interactions cause delays that reduce the
overall flow? Here, we present an experimental study of ants confronted with
two alternative routes. We find that pheromone-based attraction generates one
trail at low densities, whereas at a high level of crowding, another trail is
established before traffic volume is affected, which guarantees that an optimal
rate of food return is maintained. This bifurcation phenomenon is explained by
a nonlinear modelling approach. Surprisingly, the underlying mechanism is based
on inhibitory interactions. It implies capacity reserves, a limitation of the
density-induced speed reduction, and a sufficient pheromone concentration for
reliable trail perception. The balancing mechanism between cohesive and
dispersive forces appears to be generic in natural, urban and transportation
systems. | cond-mat_stat-mech |
Evidence of Unconventional Universality Class in a Two-Dimensional
Dimerized Quantum Heisenberg Model: The two-dimensional $J$-$J^\prime$ dimerized quantum Heisenberg model is
studied on the square lattice by means of (stochastic series expansion) quantum
Monte Carlo simulations as a function of the coupling ratio
\hbox{$\alpha=J^\prime/J$}. The critical point of the order-disorder quantum
phase transition in the $J$-$J^\prime$ model is determined as
\hbox{$\alpha_\mathrm{c}=2.5196(2)$} by finite-size scaling for up to
approximately $10 000$ quantum spins. By comparing six dimerized models we
show, contrary to the current belief, that the critical exponents of the
$J$-$J^\prime$ model are not in agreement with the three-dimensional classical
Heisenberg universality class. This lends support to the notion of nontrivial
critical excitations at the quantum critical point. | cond-mat_stat-mech |
Quantum quench dynamics in the transverse-field Ising model: A numerical
expansion in linked rectangular clusters: We study quantum quenches in the transverse-field Ising model defined on
different lattice geometries such as chains, two- and three-leg ladders, and
two-dimensional square lattices. Starting from fully polarized initial states,
we consider the dynamics of the transverse and the longitudinal magnetization
for quenches to weak, strong, and critical values of the transverse field. To
this end, we rely on an efficient combination of numerical linked cluster
expansions (NLCEs) and a forward propagation of pure states in real time. As a
main result, we demonstrate that NLCEs comprising solely rectangular clusters
provide a promising approach to study the real-time dynamics of two-dimensional
quantum many-body systems directly in the thermodynamic limit. By comparing to
existing data from the literature, we unveil that NLCEs yield converged results
on time scales which are competitive to other state-of-the-art numerical
methods. | cond-mat_stat-mech |
Velocity Distribution for Strings in Phase Ordering Kinetics: The continuity equations expressing conservation of string defect charge can
be used to find an explicit expression for the string velocity field in terms
of the order parameter in the case of an O(n) symmetric time-dependent
Ginzburg-Landau model. This expression for the velocity is used to find the
string velocity probability distribution in the case of phase-ordering kinetics
for a nonconserved order parameter. For long times $t$ after the quench,
velocities scale as $t^{-1/2}$. There is a large velocity tail in the
distribution corresponding to annihilation of defects which goes as
$V^{-(2d+2-n)}$ for both point and string defects in $d$ spatial dimensions. | cond-mat_stat-mech |
Preparation of a quantum state with one molecule at each site of an
optical lattice: Ultracold gases in optical lattices are of great interest, because these
systems bear a great potential for applications in quantum simulations and
quantum information processing, in particular when using particles with a
long-range dipole-dipole interaction, such as polar molecules. Here we show the
preparation of a quantum state with exactly one molecule at each site of an
optical lattice. The molecules are produced from an atomic Mott insulator with
a density profile chosen such that the central region of the gas contains two
atoms per lattice site. A Feshbach resonance is used to associate the atom
pairs to molecules. Remaining atoms can be removed with blast light. The
technique does not rely on the molecule-molecule interaction properties and is
therefore applicable to many systems. | cond-mat_stat-mech |
Probabilistic Breakdown Phenomenon at On-Ramp Bottlenecks in Three-Phase
Traffic Theory: A nucleation model for the breakdown phenomenon in freeway free traffic flow
at an on-ramp bottleneck is presented. This model, which can explain empirical
results on the breakdown phenomenon, is based on assumptions of three-phase
traffic theory in which the breakdown phenomenon is related to a first-order
phase transition from the "free flow" phase to the "synchronized flow" phase.
The main idea of this nucleation model is that random synchronized flow
nucleation occurs within a metastable inhomogeneous steady state associated
with a deterministic local perturbation in free flow, which can be considered
"deterministic vehicle cluster" in free flow at the bottleneck. This
deterministic vehicle cluster in free flow is motionless and exists permanent
at the bottleneck due to the on-ramp inflow. In the nucleation model, traffic
breakdown nucleation occurs through a random increase in vehicle number within
this deterministic vehicle cluster, if the amplitude of the resulting random
vehicle cluster exceeds some critical amplitude. The mean time delay and the
associated nucleation rate of speed breakdown at the bottleneck are found and
investigated. The nucleation rate of traffic breakdown as a function of the
flow rates to the on-ramp and upstream of the bottleneck is studied. The
nucleation model and the associated results exhibit qualitative different
characteristics than those found earlier in other traffic flow nucleation
models. Boundaries for speed breakdown in the diagram of congested patterns at
the bottleneck are found. These boundaries are qualitatively correlated with
numerical results of simulation of microscopic traffic flow models in the
context of three-phase traffic theory. | cond-mat_stat-mech |
Bound states of the $φ^4$ model via the nonperturbative
renormalization group: Using the nonperturbative renormalization group, we study the existence of
bound states in the symmetry-broken phase of the scalar $\phi^4$ theory in all
dimensions between two and four and as a function of the temperature. The
accurate description of the momentum dependence of the two-point function,
required to get the spectrum of the theory, is provided by means of the
Blaizot--M\'endez-Galain--Wschebor approximation scheme. We confirm the
existence of a bound state in dimension three, with a mass within 1% of
previous Monte-Carlo and numerical diagonalization values. | cond-mat_stat-mech |
Crossovers in the dynamics of supercooled liquids probed by an amorphous
wall: We study the relaxation dynamics of a binary Lennard-Jones liquid in the
presence of an amorphous wall generated from equilibrium particle
configurations. In qualitative agreement with the results presented in Nature
Phys. {\bf 8}, 164 (2012) for a liquid of harmonic spheres, we find that our
binary mixture shows a saturation of the dynamical length scale close to the
mode-coupling temperature $T_c$. Furthermore we show that, due to the broken
symmetry imposed by the wall, signatures of an additional change in dynamics
become apparent at a temperature well above $T_c$. We provide evidence that
this modification in the relaxation dynamics occurs at a recently proposed
dynamical crossover temperature $T_s > T_c$, which is related to the breakdown
of the Stokes-Einstein relation. We find that this dynamical crossover at $T_s$
is also observed for a system of harmonic spheres as well as a WCA liquid,
showing that it may be a general feature of glass-forming systems. | cond-mat_stat-mech |
The influence of absorbing boundary conditions on the transition path
times statistics: We derive an analytical expression for the transition path time (TPT)
distribution for a one-dimensional particle crossing a parabolic barrier. The
solution is expressed in terms of the eigenfunctions and eigenvalues of the
associated Fokker-Planck equation. The particle performs an anomalous dynamics
generated by a power-law memory kernel, which includes memoryless Markovian
dynamics as a limiting case. Our result takes into account absorbing boundary
conditions, extending existing results obtained for free boundaries. We show
that TPT distributions obtained from numerical simulations are in excellent
agreement with analytical results, while the typically employed free boundary
conditions lead to a systematic overestimation of the barrier height. These
findings may be useful in the analysis of experimental results on transition
path times. A web tool to perform this analysis is freely available. | cond-mat_stat-mech |
Internal energy and condensate fraction of a trapped interacting Bose
gas: We present a semiclassical two-fluid model for an interacting Bose gas
confined in an anisotropic harmonic trap and solve it in the experimentally
relevant region for a spin-polarized gas of Rb-87 atoms, obtaining the
temperature dependence of the internal energy and of the condensate fraction.
Our results are in agreement with recent experimental observations by Ensher et
al. | cond-mat_stat-mech |
Probability distributions for polymer translocation: We study the passage (translocation) of a self-avoiding polymer through a
membrane pore in two dimensions. In particular, we numerically measure the
probability distribution Q(T) of the translocation time T, and the distribution
P(s,t) of the translocation coordinate s at various times t. When scaled with
the mean translocation time <T>, Q(T) becomes independent of polymer length,
and decays exponentially for large T. The probability P(s,t) is well described
by a Gaussian at short times, with a variance that grows sub-diffusively as
t^{\alpha} with \alpha~0.8. For times exceeding <T>, P(s,t) of the polymers
that have not yet finished their translocation has a non-trivial stable shape. | cond-mat_stat-mech |
Understanding conserved amino acids in proteins: It has been conjectured that evolution exerted pressure to preserve amino
acids bearing thermodynamic, kinetic, and functional roles. In this letter we
show that the physical requirement to maintain protein stability gives rise to
a sequence conservatism pattern that is in remarkable agreement with that found
in natural proteins. Based on the physical properties of amino acids, we
propose a model of evolution that explains conserved amino acids across protein
families sharing the same fold. | cond-mat_stat-mech |
Relativistic diffusion of particles with a continuous mass spectrum: We discuss general positivity conditions necessary for a definition of a
relativistic diffusion on the phase space. We show that Lorentz covariant
random vector fields on the forward cone $p^{2}\geq 0$ lead to a definition of
a generator of Lorentz covariant diffusions. We discuss in more detail
diffusions arising from particle dynamics in a random electromagnetic field
approximating the quantum field at finite temperature. We develop statistical
mechanics of a gas of diffusing particles. We discuss viscosity of such a gas
in an expansion in gradients of the fluid velocity. | cond-mat_stat-mech |
Kinetic Equationins in the Theory of Normal Fermi Liquid: On the bases of the improved approximation for the spectral function of
one-particle states the Landau-Silin kinetic equations for the normal Fermi
liquids of neutral and electrically charged particles are shown to be valid at
finite temperature above the temperature of superfluid transition. | cond-mat_stat-mech |
Transition state theory applied to self-diffusion of hard spheres: A description in terms of transition rates among cells is used to analyze
self-diffusion of hard spheres in the fluid phase. Cell size is assumed much
larger than the mean free path. Transition state theory is used to obtain an
equation that matches numerical results previously obtained by other authors.
Two regimes are identified. For small packing fraction $\xi$, diffusion is
limited by free volume; and, for large $\xi$, diffusion is limited by velocity
autocorrelation. The expressions obtained in each regime do not require
adjustable parameters. | cond-mat_stat-mech |
Log-Poisson Statistics and Extended Self-Similarity in Driven
Dissipative Systems: The Bak-Chen-Tang forest fire model was proposed as a toy model of turbulent
systems, where energy (in the form of trees) is injected uniformly and
globally, but is dissipated (burns) locally. We review our previous results on
the model and present our new results on the statistics of the higher-order
moments for the spatial distribution of fires. We show numerically that the
spatial distribution of dissipation can be described by Log-Poisson statistics
which leads to extended self-similarity (ESS). Similar behavior is also found
in models based on directed percolation; this suggests that the concept of
Log-Poisson statistics of (appropriately normalized) variables can be used to
describe scaling not only in turbulence but also in a wide range of driven
dissipative systems. | cond-mat_stat-mech |
Phase statistics and the Hamiltonian: Modern statistical thermodynamics retains the concepts employed by Landau of
the order parameter and a functional depending on it, now called the
Hamiltonian. The present paper investigates the limits of validity for the use
of the functional to describe the statistical correlations of a thermodynamic
phase, particularly in connection with the experimentally accessible scattering
of X-rays, electrons and neutrons. Guggenheim's definition for the functional
is applied to a generalized system and the associated paradoxes are analyzed.
In agreement with Landau's original hypothesis, it is demonstrated that the
minimum is equal to the thermodynamic free energy, requiring no fluctuation
correction term. Although the fluctuation amplitude becomes large in the
vicinity of a second-order phase transition in low dimensionalities, it does
not diverge and the equilibrium order parameter remains well defined. | cond-mat_stat-mech |
Structure and Randomness of Continuous-Time Discrete-Event Processes: Loosely speaking, the Shannon entropy rate is used to gauge a stochastic
process' intrinsic randomness; the statistical complexity gives the cost of
predicting the process. We calculate, for the first time, the entropy rate and
statistical complexity of stochastic processes generated by finite unifilar
hidden semi-Markov models---memoryful, state-dependent versions of renewal
processes. Calculating these quantities requires introducing novel mathematical
objects ({\epsilon}-machines of hidden semi-Markov processes) and new
information-theoretic methods to stochastic processes. | cond-mat_stat-mech |
Enhanced stochastic oscillations in autocatalytic reactions: We study a simplified scheme of $k$ coupled autocatalytic reactions,
previously introduced by Togashi and Kaneko. The role of stochastic
fluctuations is elucidated through the use of the van Kampen system-size
expansion and the results compared with direct stochastic simulations. Regular
temporal oscillations are predicted to occur for the concentration of the
various chemical constituents, with an enhanced amplitude resulting from a
resonance which is induced by the intrinsic graininess of the system. The
associated power spectra are determined and have a different form depending on
the number of chemical constituents, $k$. We make detailed comparisons in the
two cases $k=4$ and $k=8$. Agreement between the theoretical and numerical
results for the power spectrum are good in both cases. The resulting spectrum
is especially interesting in the $k=8$ system, since it has two peaks, which
the system-size expansion is still able to reproduce accurately. | cond-mat_stat-mech |
Blocking temperature in magnetic nano-clusters: A recent study of nonextensive phase transitions in nuclei and nuclear
clusters needs a probability model compatible with the appropriate Hamiltonian.
For magnetic molecules a representation of the evolution by a Markov process
achieves the required probability model that is used to study the probability
density function (PDF) of the order parameter, i.e. the magnetization. The
existence of one or more modes in this PDF is an indication for the
superparamagnetic transition of the cluster. This allows us to determine the
factors that influence the blocking temperature, i.e. the temperature related
to the change of the number of modes in the density. It turns out that for our
model, rather than the evolution of the system implied by the Hamiltonian, the
high temperature density of the magnetization is the important factor for the
temperature of the transition. We find that an initial probability density
function with a high entropy leads to a magnetic cluster with a high blocking
temperature. | cond-mat_stat-mech |
Classical and Quantum Fluctuation Theorems for Heat Exchange: The statistics of heat exchange between two classical or quantum finite
systems initially prepared at different temperatures are shown to obey a
fluctuation theorem. | cond-mat_stat-mech |
A Cluster Expansion for Dipole Gases: We give a new proof of the well-known upper bound on the correlation function
of a gas of non-overlapping dipoles of fixed length and discrete orientation
working directly in the charge representation, instead of the more usual
sine-Gordon representation. | cond-mat_stat-mech |
Dynamical signatures of molecular symmetries in nonequilibrium quantum
transport: Symmetries play a crucial role in ubiquitous systems found in Nature. In this
work, we propose an elegant approach to detect symmetries by measuring quantum
currents. Our detection scheme relies on initiating the system in an
anti-symmetric initial condition, with respect to the symmetric sites, and
using a probe that acts like a local noise. Depending on the position of the
probe the currents exhibit unique signatures such as a quasi-stationary plateau
indicating the presence of meta-stability and multi-exponential decays in case
of multiple symmetries. The signatures are sensitive to the probe and vanish
completely when the timescale of the coherent system dynamics is much longer
than the timescale of the probe. These results are demonstrated using a
$4$-site model and an archetypal example of the para-benzene ring and are shown
to be robust under a weak disorder. | cond-mat_stat-mech |
Progressive quenching --- Ising chain models: Of the Ising spin chain with the nearest neighbor or up to the second nearest
neighbor interactions, we fixed progressively either a single spin or a pair of
neighboring spins at the value they took. Before the subsequent fixation, the
unquenched part of the system is equilibrated. We found that, in all four
combinations of the cases, the ensemble of quenched spin configurations is the
equilibrium ensemble. | cond-mat_stat-mech |
Kinetic Theory and Hydrodynamics for a Low Density Gas: Many features of real granular fluids under rapid flow are exhibited as well
by a system of smooth hard spheres with inelastic collisions. For such a
system, it is tempting to apply standard methods of kinetic theory and
hydrodynamics to calculate properties of interest. The domain of validity for
such methods is a priori uncertain due to the inelasticity, but recent
systematic studies continue to support the utility of kinetic theory and
hydrodynamics as both qualitative and quantitative descriptions for many
physical states. The basis for kinetic theory and hydrodynamic descriptions is
discussed briefly for the special case of a low density gas. | cond-mat_stat-mech |
Optimization and Growth in First-Passage Resetting: We combine the processes of resetting and first-passage to define
\emph{first-passage resetting}, where the resetting of a random walk to a fixed
position is triggered by a first-passage event of the walk itself. In an
infinite domain, first-passage resetting of isotropic diffusion is
non-stationary, with the number of resetting events growing with time as
$\sqrt{t}$. We calculate the resulting spatial probability distribution of the
particle analytically, and also obtain this distribution by a geometric path
decomposition. In a finite interval, we define an optimization problem that is
controlled by first-passage resetting; this scenario is motivated by
reliability theory. The goal is to operate a system close to its maximum
capacity without experiencing too many breakdowns. However, when a breakdown
occurs the system is reset to its minimal operating point. We define and
optimize an objective function that maximizes the reward (being close to
maximum operation) minus a penalty for each breakdown. We also investigate
extensions of this basic model to include delay after each reset and to two
dimensions. Finally, we study the growth dynamics of a domain in which the
domain boundary recedes by a specified amount whenever the diffusing particle
reaches the boundary after which a resetting event occurs. We determine the
growth rate of the domain for the semi-infinite line and the finite interval
and find a wide range of behaviors that depend on how much the recession occurs
when the particle hits the boundary. | cond-mat_stat-mech |
Mean trapping time for an arbitrary node on regular hyperbranched
polymers: The regular hyperbranched polymers (RHPs), also known as Vicsek fractals, are
an important family of hyperbranched structures which have attracted a wide
spread attention during the past several years. In this paper, we study the
first-passage properties for random walks on the RHPs. Firstly, we propose a
way to label all the different nodes of the RHPs and derive exact formulas to
calculate the mean first-passage time (MFPT) between any two nodes and the mean
trapping time (MTT) for any trap node. Then, we compare the trapping efficiency
between any two nodes of the RHPs by using the MTT as the measures of trapping
efficiency. We find that the central node of the RHPs is the best trapping site
and the nodes which are the farthest nodes from the central node are the worst
trapping sites. Furthermore, we find that the maximum of the MTT is about $4$
times more than the minimum of the MTT. The result is similar to the results in
the recursive fractal scale-free trees and T-fractal, but it is quite different
from that in the recursive non-fractal scale-free trees. These results can help
understanding the influences of the topological properties and trap location on
the trapping efficiency. | cond-mat_stat-mech |
Thermodynamic model for the glass transition: deeply supercooled liquids
as mixtures of solid-like and liquid-like micro-regions: For a deeply supercooled liquid just above its glass transition temperature,
we present a simple thermodynamic model, where the deeply supercooled liquid is
assumed to be a mixture of solid-like and liquid-like micro regions. The mole
fraction of the liquid-like regions controls the thermodynamic properties of
the supercooled liquid while that of the solid-like regions controls its
relaxation time or viscosity. From the universal temperature dependence of the
molar excess entropy for the deeply supercooled liquids, we derive the
temperature dependence of the mole fraction of the liquid-like regions to
obtain the universal temperature dependence of the relaxation time or the
viscosity for the deeply supercooled liquids. A central parameter of our model
is then shown to be a measure for the fragility of a supercooled liquid. We
also suggest a way to test our physical picture of deeply supercooled liquids
by means of molecular dynamics simulations of model liquids. | cond-mat_stat-mech |
Systematic perturbation approach for a dynamical scaling law in a
kinetically constrained spin model: The dynamical behaviours of a kinetically constrained spin model
(Fredrickson-Andersen model) on a Bethe lattice are investigated by a
perturbation analysis that provides exact final states above the nonergodic
transition point. It is observed that the time-dependent solutions of the
derived dynamical systems obtained by the perturbation analysis become
systematically closer to the results obtained by Monte Carlo simulations as the
order of a perturbation series is increased. This systematic perturbation
analysis also clarifies the existence of a dynamical scaling law, which
provides a implication for a universal relation between a size scale and a time
scale near the nonergodic transition. | cond-mat_stat-mech |
Statistical mechanical approach of complex networks with weighted links: Systems which consist of many localized constituents interacting with each
other can be represented by complex networks. Consistently, network science has
become highly popular in vast fields focusing on natural, artificial and social
systems. We numerically analyze the growth of $d$-dimensional geographic
networks (characterized by the index $\alpha_G\geq0$; $d = 1, 2, 3, 4$) whose
links are weighted through a predefined random probability distribution, namely
$P(w) \propto e^{-|w - w_c|/\tau}$, $w$ being the weight $ (w_c \geq 0; \; \tau
> 0)$. In this model, each site has an evolving degree $k_i$ and a local energy
$\varepsilon_i \equiv \sum_{j=1}^{k_i} w_{ij}/2$ ($i = 1, 2, ..., N$) that
depend on the weights of the links connected to it. Each newly arriving site
links to one of the pre-existing ones through preferential attachment given by
the probability $\Pi_{ij}\propto \varepsilon_{i}/d^{\,\alpha_A}_{ij}
\;\;(\alpha_A \ge 0)$, where $d_{ij}$ is the Euclidean distance between the
sites. Short- and long-range interactions respectively correspond to
$\alpha_A/d>1$ and $0\leq \alpha_A/d \leq 1$; $\alpha_A/d \to \infty$
corresponds to interactions between close neighbors, and $\alpha_A/d \to 0$
corresponds to infinitely-ranged interactions. The site energy distribution
$p(\varepsilon)$ corresponds to the usual degree distribution $p(k)$ as the
particular instance $(w_c,\tau)=(2,0)$. We numerically verify that the
corresponding connectivity distribution $p(\varepsilon)$ converges, when
$\alpha_A/d\to\infty$, to the weight distribution $P(w)$ for infinitely narrow
distributions (i.e., $\tau \to \infty, \,\forall w_c$) as well as for $w_c\to0,
\, \forall\tau$. | cond-mat_stat-mech |
Effective interaction between guest charges immersed in 2D jellium: The model under study is an infinite 2D jellium of pointlike particles with
elementary charge $e$, interacting via the logarithmic potential and in thermal
equilibrium at the inverse temperature $\beta$. Two cases of the coupling
constant $\Gamma\equiv \beta e^2$ are considered: the Debye-H\"uckel limit
$\Gamma\to 0$ and the free-fermion point $\Gamma=2$. In the most general
formulation, two guest particles, the one with charge $q e$ (the valence $q$
being an arbitrary integer) and the hard core of radius $\sigma>0$ and the
pointlike one with elementary charge $e$, are immersed in the bulk of the
jellium at distance $d\ge \sigma$. Two problems are of interest: the asymptotic
large-distance behavior of the excess charge density induced in the jellium and
the effective interaction between the guest particles. Technically, the induced
charge density and the effective interaction are expressed in terms of
multi-particle correlations of the pure (translationally invariant) jellium
system. It is shown that the separation form of the induced charge density onto
its radial and angle parts, observed previously in the limit $\Gamma\to 0$, is
not reproduced at the coupling $\Gamma=2$. Based on an exact expression for the
effective interaction between guest particles at $\Gamma=2$, oppositely
($q=0,-1,-2,\ldots$) charged guest particles always attract one another while
likely ($q=1,2,\ldots$) charged guest particles repeal one another up to a
certain distance $d$ between them and then the mutual attraction takes place up
to asymptotically large (finite) distances. | cond-mat_stat-mech |
Ballistic aggregation: a solvable model of irreversible many particles
dynamics: The adhesive dynamics of a one-dimensional aggregating gas of point particles
is rigorously described. The infinite hierarchy of kinetic equations for the
distributions of clusters of nearest neighbours is shown to be equivalent to a
system of two coupled equations for a large class of initial conditions. The
solution to these nonlinear equations is found by a direct construction of the
relevant probability distributions in the limit of a continuous initial mass
distribution. We show that those limiting distributions are identical to those
of the statistics of shocks in the Burgers turbulence. The analysis relies on a
mapping on a Brownian motion problem with parabolic constraints. | cond-mat_stat-mech |
Vicinal surface growth: bunching and meandering instabilities: The morphology of a growing crystal surface is studied in the case of an
unstable two-dimensional step flow. Competition between bunching and meandering
of steps leads to a variety of patterns characterized by their respective
instability growth rates. The roughness exponent is shown to go from 1/2 to 1,
between the pure bunching to the meandering regimes. Using numerical
simulations, we observe that generically, a transition between the two regimes
occurs. We find surface shapes and roughness time evolution in quantitative
agreement with experiments. | cond-mat_stat-mech |
Entropies for complex systems: generalized-generalized entropies: Many complex systems are characterized by non-Boltzmann distribution
functions of their statistical variables. If one wants to -- justified or not
-- hold on to the maximum entropy principle for complex statistical systems
(non-Boltzmann) we demonstrate how the corresponding entropy has to look like,
given the form of the corresponding distribution functions. By two natural
assumptions that (i) the maximum entropy principle should hold and that (ii)
entropy should describe the correct thermodynamics of a system (which produces
non-Boltzmann distributions) the existence of a class of fully consistent
entropies can be deduced. Classical Boltzmann-Gibbs entropy is recovered as a
special case for the observed distribution being the exponential, Tsallis
entropy is the special case for q-exponential observations. | cond-mat_stat-mech |
Open statistical ensemble and surface phenomena: In the present work we investigate a new statistical ensemble, which seems
logical to be entitled the open one, for the case of a one-component system of
ordinary particles. Its peculiarity is in complementing the consideration of a
system with the inclusion of a certain surrounding area. The calculations
indicate the necessity of taking into account the surface that delimits a given
system even in the case when the latter is a part of a uniform medium and is
not singled out one way or another.
The surface tension coefficient behaves unlike two-phase systems in
equilibrium and depends on two variables - pressure as well as temperature -
and belongs to the boundary separating a hard solid from a fluid. As for the
mathematical mechanism ensuring the fulfillment of thermodynamic relations, the
emphasis is shifted from operating with series, like in the grand canonical
ensemble, towards employing the recurrence relations of a new class of
functions that incorporate Boltzmann and Ursell factors as their extreme cases
and towards utilizing generating functions.
The second topic of discussion that the present article deals with is the
consideration of the surface tension and adsorption observed at the boundary of
a solid body and a liquid or gas carried out on the basis of the analysis of
the classical system found in a field of force of general type. The surface
terms are calculated with the aid of field functions and the correlation
functions of an unperturbed volume phase and behave somewhat vaguely;
particularly, as a function of activity, they may start with a linear or
quadratic term. | cond-mat_stat-mech |
An Explicit Form of the Equation of Motion of the Interface in
Bicontinuous Phases: The explicit form of the interface equation of motion derived assuming a
minimal surface is extended to general bicontinuous interfaces that appear in
the diffusion limited stage of the phase separation process of binary mixtures.
The derivation is based on a formal solution of the equivalent simple layer for
the Dirichlet problem of the Laplace equation with an arbitrary boundary
surface. It is shown that the assumption of a minimal surface used in the
previous linear theory is not necessary, but its bicontinuous nature is the
essential condition required for us to rederive the explicit form of the simple
layer. The de- rived curvature flow equation has a phenomenological cut-off
length, i.e., an `electro-static' screening length. That is re- lated to the
well-known scaling length characterizing the spatial pattern size of a
homogeneously growing bicontinuous phase. The corresponding equation of the
level function in this scheme is given in a one-parameter form also. | cond-mat_stat-mech |
The thermal denaturation of DNA studied with neutron scattering: The melting transition of deoxyribonucleic acid (DNA), whereby the strands of
the double helix structure completely separate at a certain temperature, has
been characterized using neutron scattering. A Bragg peak from B-form fibre DNA
has been measured as a function of temperature, and its widths and integrated
intensities have been interpreted using the Peyrard-Bishop-Dauxois (PBD) model
with only one free parameter. The experiment is unique, as it gives spatial
correlation along the molecule through the melting transition where other
techniques cannot. | cond-mat_stat-mech |
Exact Density Functionals in One Dimension: We propose a new and general method for deriving exact density functionals in
one dimension for lattice gases with finite-range pairwise interactions.
Corresponding continuum functionals are derived by applying a proper limiting
procedure. The method is based on a generalised Markov property, which allows
us to set up a rather transparent scheme that covers all previously known exact
functionals for one-dimensional lattice gas or fluid systems. Implications for
a systematic construction of approximate density functionals in higher
dimensions are pointed out. | cond-mat_stat-mech |
Quantum critical systems with dissipative boundaries: We study the effects of dissipative boundaries in many-body systems at
continuous quantum transitions, when the parameters of the Hamiltonian driving
the unitary dynamics are close to their critical values. As paradigmatic
models, we consider fermionic wires subject to dissipative interactions at the
boundaries, associated with pumping or loss of particles. They are induced by
couplings with a Markovian baths, so that the evolution of the system density
matrix can be described by a Lindblad master equation. We study the quantum
evolution arising from variations of the Hamiltonian and dissipation
parameters, starting at t=0 from the ground state of the critical Hamiltonian.
Two different dynamic regimes emerge: (i) an early-time regime for times t ~ L,
where the competition between coherent and incoherent drivings develops a
dynamic finite-size scaling, obtained by extending the scaling framework
describing the coherent critical dynamics of the closed system, to allow for
the boundary dissipation; (ii) a large-time regime for t ~ L^3 whose dynamic
scaling describes the late quantum evolution leading to the t->infty stationary
states. | cond-mat_stat-mech |
Ripening and Focusing of Aggregate Size Distributions with Overall
Volume Growth: We explore the evolution of the aggregate size distribution in systems where
aggregates grow by diffusive accretion of mass. Supersaturation is controlled
in such a way that the overall aggregate volume grows linearly in time.
Classical Ostwald ripening, which is recovered in the limit of vanishing
overall growth, constitutes an unstable solution of the dynamics. In the
presence of overall growth evaporation of aggregates always drives the dynamics
into a new, qualitatively different growth regime where ripening ceases, and
growth proceeds at a constant number density of aggregates. We provide a
comprehensive description of the evolution of the aggregate size distribution
in the constant density regime: the size distribution does not approach a
universal shape, and even for moderate overall growth rates the standard
deviation of the aggregate radius decays monotonically. The implications of
this theory for the focusing of aggregate size distributions are discussed for
a range of different settings including the growth of tiny rain droplets in
clouds, as long as they do not yet feel gravity, and the synthesis of
nano-particles and quantum dots. | cond-mat_stat-mech |
Irreversible mesoscale fluctuations herald the emergence of dynamical
phases: We study fluctuating field models with spontaneously emerging dynamical
phases. We consider two typical transition scenarios associated with
parity-time symmetry breaking: oscillatory instabilities and critical
exceptional points. An analytical investigation of the low-noise regime reveals
a drastic increase of the mesoscopic entropy production toward the transitions.
For an illustrative model of two nonreciprocally coupled Cahn-Hilliard fields,
we find physical interpretations in terms of actively propelled interfaces and
a coupling of modes near the critical exceptional point. | cond-mat_stat-mech |
Nonadditivity in Quasiequilibrium States of Spin Systems with Lattice
Distortion: It is pointed out that there exists a short-range interacting system, i.e.
the elastic spin model, which is extensive but nonadditive. It is numerically
shown that, depending on the statistical ensemble, the specific heat or the
susceptibility becomes negative in a certain parameter region, which shows
ensemble inequivalence in this model. Further, we numerically estimate the
effective Hamiltonian for spin variables, and it is clarified that the
effective interaction among spin variables is long-ranged. Remarkably, the so
called Kac's prescription, which is usually regarded as a mathematical
operation to make the system extensive, naturally holds in the effective
interaction. | cond-mat_stat-mech |
Majority Rule Dynamics in Finite Dimensions: We investigate the long-time behavior of a majority rule opinion dynamics
model in finite spatial dimensions. Each site of the system is endowed with a
two-state spin variable that evolves by majority rule. In a single update
event, a group of spins with a fixed (odd) size is specified and all members of
the group adopt the local majority state. Repeated application of this update
step leads to a coarsening mosaic of spin domains and ultimate consensus in a
finite system. The approach to consensus is governed by two disparate time
scales, with the longer time scale arising from realizations in which spins
organize into coherent single-opinion bands. The consequences of this
geometrical organization on the long-time kinetics are explored. | cond-mat_stat-mech |
Macroscopic Fluctuation Theory and Current Fluctuations in Active
Lattice Gases: We study the current large deviations for a lattice model of interacting
active particles displaying a motility-induced phase separation (MIPS). To do
this, we first derive the exact fluctuating hydrodynamics of the model in the
large system limit. On top of the usual Gaussian noise terms the theory also
presents Poissonian noise terms, that we fully account for. We find a dynamical
phase transition between flat density profiles and sharply phase-separated
traveling waves, and we derive the associated phase diagram together with the
large deviation function for all phases, including the one displaying MIPS. We
show how the results can be obtained using methods similar to those of
equilibrium phase separation, in spite of the nonequilibrium nature of the
problem. | cond-mat_stat-mech |
From regular to growing small-world networks: We propose a growing model which interpolates between one-dimensional regular
lattice and small-world networks. The model undergoes an interesting phase
transition from large to small world. We investigate the structural properties
by both theoretical predictions and numerical simulations. Our growing model is
a complementarity for the famous static WS network model. | cond-mat_stat-mech |
Reference Distribution Functions for Magnetically Confined Plasmas from
the Minimum Entropy Production Theorem and the MaxEnt Principle, subject to
the Scale-Invariant Restrictions: We derive the expression of the reference distribution function for
magnetically confined plasmas far from the thermodynamic equilibrium. The local
equilibrium state is fixed by imposing the minimum entropy production theorem
and the maximum entropy (MaxEnt) principle, subject to scale invariance
restrictions. After a short time, the plasma reaches a state close to the local
equilibrium. This state is referred to as the reference state. The aim of this
letter is to determine the reference distribution function (RDF) when the local
equilibrium state is defined by the above mentioned principles. We prove that
the RDF is the stationary solution of a generic family of stochastic processes
corresponding to an universal Landau-type equation with white parametric noise.
As an example of application, we consider a simple, fully ionized, magnetically
confined plasmas, with auxiliary Ohmic heating. The free parameters are linked
to the transport coefficients of the magnetically confined plasmas, by the
kinetic theory. | cond-mat_stat-mech |
Division of Labor as the Result of Phase Transition: The emergence of labor division in multi-agent system is analyzed by the
method of statistical physics. Considering a system consists of N homogeneous
agents. Their behaviors are determined by the returns from their production.
Using the Metropolis method in statistical physics, which in this model can
been regarded as a kind of uncertainty in decision making, we constructed a
Master equation model to describe the evolution of the agents distribution.
When we introduce the mechanism of learning by doing to describe the effect of
technical progress and a formula for the competitive cooperation, the model
gives us the following interesting results: (1) As the results of long term
evolution, the system can reach a steady state. (2) When the parameters exceed
a critical point, the labor division emerges as the result of phase transition.
(3) Although the technical progress decides whether or not phase transition
occurs, the critical point is strongly effected by the competitive cooperation.
From the above physical model and the corresponding results, we can get a
more deeply understanding about the labor division. | cond-mat_stat-mech |
Quantum Stochastic Synchronization: We study within the spin-boson dynamics the synchronization of quantum
tunneling with an external periodic driving signal. As a main result we find
that at a sufficiently large system-bath coupling strength (Kondo parameter
a>1) the thermal noise plays a constructive role in yielding both a frequency
and a phase synchronization in a symmetric two-level system. Such riveting
synchronization occurs when the driving frequency supersedes the zero
temperature tunneling rate. As an application evidencing the effect, we
consider a charge transfer dynamics in molecular complexes. | cond-mat_stat-mech |
Reply to Comment on Nonlocal quartic interactions and universality
classes in perovskite manganites: Comment [arXiv:cond-mat.stat.mech., 1602.02087v1 (2016)] has raised questions
claiming that the nonlocal model Hamiltonian presented in [Phys. Rev. E 92,
012123 (2015)] is equivalent to the standard (short-ranged) \Phi^4 theory.
These claims are based on a low momentum expansion of the interaction vertex
that cannot be applied to the vertex factors containing both low and high
momenta inside the loop-integrals. Elaborating upon the important steps of the
momentum shell decimation scheme, employed in the renormalization-group
calculation, we explicitly show the interplay of internal (high) and external
(low) momenta determining the loop integrals for self-energy and vertex
functions giving rise to corrections (to the bare parameters) different from
those of the standard (short-ranged) \Phi^4 theory. Employing explicit
mathematical arguments, we show that this difference persists when the range of
interaction is assumed to be long (short) ranged with respect to the lattice
constant (correlation-length), yielding the critical exponents as given in the
original paper. | cond-mat_stat-mech |
Comment on ``Fragmented Condensate Ground State of Trapped Weakly
Interacting Bosons in Two Dimensions": Recently Liu et al. [PRL 87, 030404 (2001)] examined the lowest state of a
weakly-interacting Bose-Einstein condensate. In addition to other interesting
results, using the method of the pair correlation function, they questioned the
validity of the mean-field picture of the formation of vortices and stated that
the vortices are generated at the center of the cloud. This is in apparent
contradiction to the Gross-Pitaevskii approach, which predicts that the
vortices successively enter the cloud from its outer parts as L/N (where N is
the number of atoms in the trap and hbar(L) is the angular momentum of the
system) increases. We have managed to reproduce the results of Liu et al.
however a more careful analysis presented below confirms the validity of the
mean-field approach. | cond-mat_stat-mech |
A comprehensive scenario of the thermodynamic anomalies of water using
the TIP4P/2005 model: The striking behavior of water has deserved it to be referred to as an
"anomalous" liquid. The water anomalies are greatly amplified in metastable
(supercooled/stretched) regions. This makes difficult a complete experimental
description since, beyond certain limits, the metastable phase necessarily
transforms into the stable one. Theoretical interpretation of the water
anomalies could then be based on simulation results of well validated water
models. But the analysis of the simulations has not yet reached a consensus. In
particular, one of the most popular theoretical scenarios -involving the
existence of a liquid-liquid critical point (LLCP)- is disputed by several
authors. In this work we propose to use a number of exact thermodynamic
relations which can be tested in a region of the phase diagram outside the LLCP
thus avoiding the problems associated to the coexistence region. The central
property connected to other water anomalies is the locus of temperatures at
which the density along isobars attain a maximum (TMD line) or a minimum (TmD),
computed via simulations for a successful water model, TIP4P/2005. Next, we
have evaluated the vapor-liquid spinodal in the region of large negative
pressures. The shape of these curves and their connection to the extrema of
response functions (isothermal compressibility and heat capacity at constant
pressure) may help to elucidate the validity of the theoretical proposals. In
this way we are able to present for the first time a comprehensive scenario of
the thermodynamic water anomalies for TIP4P/2005 and their relation to the
vapor-liquid spinodal. The overall picture shows a remarkable similarity with
the corresponding one for the ST2 water model, for which the existence of a
LLCP has been demonstrated in recent years. It also provides a hint as to where
the long-sought for extrema in response functions might become accessible to
experiments. | cond-mat_stat-mech |
Nonstandard entropy production in the standard map: We investigate the time evolution of the entropy for a paradigmatic
conservative dynamical system, the standard map, for different values of its
controlling parameter $a$. When the phase space is sufficiently ``chaotic''
(i.e., for large $|a|$), we reproduce previous results. For small values of
$|a|$, when the phase space becomes an intricate structure with the coexistence
of chaotic and regular regions, an anomalous regime emerges. We characterize
this anomalous regime with the generalized nonextensive entropy, and we observe
that for values of $a$ approaching zero, it lasts for an increasingly large
time. This scenario displays a striking analogy with recent observations made
in isolated classical long-range $N$-body Hamiltonians, where, for a large
class of initial conditions, a metastable state (whose duration diverges with
$1/N\to 0$) is observed before it crosses over to the usual, Boltzmann-Gibbs
regime. | cond-mat_stat-mech |
Thermodynamics of emergent structure in active matter: Active matter is rapidly becoming a key paradigm of out-of-equilibrium soft
matter exhibiting complex collective phenomena, yet the thermodynamics of such
systems remain poorly understood. In this letter we study the nonequilbrium
thermodynamics of large scale active systems capable of mobility-induced phase
separation and polar alignment, using a fully under-damped model which exhibits
hidden entropy productions not previously reported in the literature. We
quantify steady state entropy production at each point in the phase diagram,
revealing characteristic dissipation rates associated with the distinct phases
and configurational structure. This reveals sharp discontinuities in the
entropy production at phase transitions and facilitates identification of the
thermodynamics of micro-features, such as defects in the emergent structure.
The interpretation of the time reversal symmetry in the dynamics of the
particles is found to be crucial. | cond-mat_stat-mech |
Nonlinear integral equations for thermodynamics of the sl(r+1)
Uimin-Sutherland model: We derive traditional thermodynamic Bethe ansatz (TBA) equations for the
sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer
matrix. These TBA equations are identical to the ones from the string
hypothesis. Next we derive a new family of nonlinear integral equations (NLIE).
In particular, a subset of these NLIE forms a system of NLIE which contains
only a finite number of unknown functions. For r=1, this subset of NLIE reduces
to Takahashi's NLIE for the XXX spin chain. A relation between the traditional
TBA equations and our new NLIE is clarified. Based on our new NLIE, we also
calculate the high temperature expansion of the free energy. | cond-mat_stat-mech |
Phase diagram and structural diversity of the densest binary sphere
packings: The densest binary sphere packings have historically been very difficult to
determine. The only rigorously known packings in the alpha-x plane of sphere
radius ratio alpha and relative concentration x are at the Kepler limit alpha =
1, where packings are monodisperse. Utilizing an implementation of the
Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E
82, 061302 (2010)], we present the most comprehensive determination to date of
the phase diagram in (alpha,x) for the densest binary sphere packings.
Unexpectedly, we find many distinct new densest packings. | cond-mat_stat-mech |
Size Segregation of Granular Matter in Silo Discharges: We present an experimental study of segregation of granular matter in a
quasi-two dimensional silo emptying out of an orifice. Size separation is
observed when multi-sized particles are used with the larger particles found in
the center of the silo in the region of fastest flow. We use imaging to study
the flow inside the silo and quantitatively measure the concentration profiles
of bi-disperse beads as a function of position and time. The angle of the
surface is given by the angle of repose of the particles, and the flow occurs
in a few layers only near the top of this inclined surface. The flowing region
becomes deeper near the center of the silo and is confined to a parabolic
region centered at the orifice which is approximately described by the
kinematic model. The experimental evidence suggests that the segregation occurs
on the surface and not in the flow deep inside the silo where velocity
gradients also are present. We report the time development of the
concentrations of the bi-disperse particles as a function of size ratios, flow
rate, and the ratio of initial mixture. The qualitative aspects of the observed
phenomena may be explained by a void filling model of segregation. | cond-mat_stat-mech |
Size effects on generation recombination noise: We carry out an analytical theory of generation-recombination noise for a two
level resistor model which goes beyond those presently available by including
the effects of both space charge fluctuations and diffusion current. Finite
size effects are found responsible for the saturation of the low frequency
current spectral density at high enough applied voltages. The saturation
behaviour is controlled essentially by the correlations coming from the long
range Coulomb interaction. It is suggested that the saturation of the current
fluctuations for high voltage bias constitutes a general feature of
generation-recombination noise. | cond-mat_stat-mech |
General Structural Results for Potts Model Partition Functions on
Lattice Strips: We present a set of general results on structural features of the $q$-state
Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature
Boltzmann variable $v$ for various lattice strips of arbitrarily great width
$L_y$ vertices and length $L_x$ vertices, including (i) cyclic and M\"obius
strips of the square and triangular lattice, and (ii) self-dual cyclic strips
of the square lattice. We also present an exact solution for the chromatic
polynomial for the cyclic and M\"obius strips of the square lattice with width
$L_y=5$ (the greatest width for which an exact solution has been obtained so
far for these families). In the $L_x \to \infty$ limit, we calculate the
ground-state degeneracy per site, $W(q)$ and determine the boundary ${\cal B}$
across which $W(q)$ is singular in the complex $q$ plane. | cond-mat_stat-mech |
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