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The relaxation dynamics of a viscous silica melt: II The intermediate
scattering functions: We use molecular dynamics computer simulations to study the relaxation
dynamics of a viscous melt of silica. The coherent and incoherent intermediate
scattering functions, F_d(q,t) and F_s(q,t), show a crossover from a nearly
exponential decay at high temperatures to a two-step relaxation at low
temperatures. Close to the critical temperature of mode-coupling theory (MCT)
the correlators obey in the alpha-regime the time temperature superposition
principle (TTSP) and show a weak stretching. We determine the wave-vector
dependence of the stretching parameter and find that for F_d(q,t) it shows
oscillations which are in phase with the static structure factor. The
temperature dependence of the alpha- relaxation times tau shows a crossover
from an Arrhenius law at low temperatures to a weaker T-dependence at
intermediate and high temperatures. At the latter temperatures the T-dependence
is described well by a power law. We find that the exponent gamma of the power
law for tau are significantly larger than the one for the diffusion constant.
The q-dependence of the alpha-relaxation times for F_d(q,t) oscillates around
tau(q) for F_s(q,t) and is in phase with the structure factor. Due to the
strong vibrational component of the dynamics at short times the TTSP is not
valid in the beta- relaxation regime. We show, however, that in this time
window the shape of the curves is independent of the correlator and is given by
a functional form proposed by MCT. We find that the value of the von Schweidler
exponent and the value of gamma for finite q are compatible with the expression
proposed by MCT. We conclude that, in the temperature regime where the
relaxation times are mesoscopic, many aspects of the dynamics of this strong
glass former can be rationalized very well by MCT. | cond-mat_stat-mech |
Attractive and repulsive polymer-mediated forces between scale-free
surfaces: We consider forces acting on objects immersed in, or attached to, long
fluctuating polymers. The confinement of the polymer by the obstacles results
in polymer-mediated forces that can be repulsive (due to loss of entropy) or
attractive (if some or all surfaces are covered by adsorbing layers). The
strength and sign of the force in general depends on the detailed shape and
adsorption properties of the obstacles, but assumes simple universal forms if
characteristic length scales associated with the objects are large. This occurs
for scale-free shapes (such as a flat plate, straight wire, or cone), when the
polymer is repelled by the obstacles, or is marginally attracted to it (close
to the depinning transition where the absorption length is infinite). In such
cases, the separation $h$ between obstacles is the only relevant macroscopic
length scale, and the polymer mediated force equals ${\cal A} \, k_{B}T/h$,
where $T$ is temperature. The amplitude ${\cal A}$ is akin to a critical
exponent, depending only on geometry and universality of the polymer system.
The value of ${\cal A}$, which we compute for simple geometries and ideal
polymers, can be positive or negative. Remarkably, we find ${\cal A}=0$ for
ideal polymers at the adsorption transition point, irrespective of shapes of
the obstacles, i.e. at this special point there is no polymer-mediated force
between obstacles (scale-free or not). | cond-mat_stat-mech |
Cooperative Transport of Brownian Particles: We consider the collective motion of finite-sized, overdamped Brownian
particles (e.g., motor proteins) in a periodic potential. Simulations of our
model have revealed a number of novel cooperative transport phenomena,
including (i) the reversal of direction of the net current as the particle
density is increased and (ii) a very strong and complex dependence of the
average velocity on both the size and the average distance of the particles. | cond-mat_stat-mech |
On controlling simple dynamics by a disagreement function: We introduce a formula for the disagreement function which is used to control
a recently proposed dynamics of the Ising spin system. This leads to four
different phases of the Ising spin chain in a zero temperature. One of these
phases is doubly degenerated (anti- and ferromagnetic states are equally
probable). On the borders between the phases two types of transitions are
observed: infinite degeneration and instability lines. The relaxation of the
system depends strongly on the phase. | cond-mat_stat-mech |
Statistics of the work done by splitting a one-dimensional
quasi-condensate: Motivated by experiments on splitting one-dimensional quasi-condensates, we
study the statistics of the work done by a quantum quench in a bosonic system.
We discuss the general features of the probability distribution of the work and
focus on its behaviour at the lowest energy threshold, which develops an edge
singularity. A formal connection between this probability distribution and the
critical Casimir effect in thin classical films shows that certain features of
the edge singularity are universal as the post-quench gap tends to zero. Our
results are quantitatively illustrated by an exact calculation for
non-interacting bosonic systems. The effects of finite system size,
dimensionality, and non-zero initial temperature are discussed in detail. | cond-mat_stat-mech |
Domain-wall structure of a classical Heisenberg ferromagnet on a Mobius
strip: We study theoretically the structure of domain walls in ferromagnetic states
on Mobius strips. A two-dimensional classical Heisenberg ferromagnet with
single-site anisotropy is treated within a mean-field approximation by taking
into account the boundary condition to realize the Mobius geometry. It is found
that two types of domain walls can be formed, namely, parallel or perpendicular
to the circumference, and that the relative stability of these domain walls is
sensitive to the change in temperature and an applied magnetic field. The
magnetization has a discontinuity as a function of temperature and the external
field. | cond-mat_stat-mech |
Legendre transform structure and extremal properties of the relative
Fisher information: Variational extremization of the relative Fisher information (RFI, hereafter)
is performed. Reciprocity relations, akin to those of thermodynamics are
derived, employing the extremal results of the RFI expressed in terms of
probability amplitudes. A time independent Schr\"{o}dinger-like equation
(Schr\"{o}dinger-like link) for the RFI is derived. The concomitant Legendre
transform structure (LTS, hereafter) is developed by utilizing a generalized
RFI-Euler theorem, which shows that the entire mathematical structure of
thermodynamics translates into the RFI framework, both for equilibrium and
non-equilibrium cases. The qualitatively distinct nature of the present results
\textit{vis-\'{a}-vis} those of prior studies utilizing the Shannon entropy
and/or the Fisher information measure (FIM, hereafter) is discussed. A
principled relationship between the RFI and the FIM frameworks is derived. The
utility of this relationship is demonstrated by an example wherein the energy
eigenvalues of the Schr\"{o}dinger-like link for the RFI is inferred solely
using the quantum mechanical virial theorem and the LTS of the RFI. | 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 |
Randomly dilute Ising model: A nonperturbative approach: The N-vector cubic model relevant, among others, to the physics of the
randomly dilute Ising model is analyzed in arbitrary dimension by means of an
exact renormalization-group equation. This study provides a unified picture of
its critical physics between two and four dimensions. We give the critical
exponents for the three-dimensional randomly dilute Ising model which are in
good agreement with experimental and numerical data. The relevance of the cubic
anisotropy in the O(N) model is also treated. | cond-mat_stat-mech |
Optimal tuning of a confined Brownian information engine: A Brownian information engine is a device extracting a mechanical work from a
single heat bath by exploiting the information on the state of a Brownian
particle immersed in the bath. As for engines, it is important to find the
optimal operating condition that yields the maximum extracted work or power.
The optimal condition for a Brownian information engine with a finite cycle
time $\tau$ has been rarely studied because of the difficulty in finding the
nonequilibrium steady state. In this study, we introduce a model for the
Brownian information engine and develop an analytic formalism for its steady
state distribution for any $\tau$. We find that the extracted work per engine
cycle is maximum when $\tau$ approaches infinity, while the power is maximum
when $\tau$ approaches zero. | cond-mat_stat-mech |
Correlation functions of the integrable spin-s chain: We study the correlation functions of su(2) invariant spin-s chains in the
thermodynamic limit. We derive non-linear integral equations for an auxiliary
correlation function $\omega$ for any spin s and finite temperature T. For the
spin-3/2 chain for arbitrary temperature and zero magnetic field we obtain
algebraic expressions for the reduced density matrix of two-sites. In the zero
temperature limit, the density matrix elements are evaluated analytically and
appear to be given in terms of Riemann's zeta function values of even and odd
arguments. | cond-mat_stat-mech |
Investigation of the seismicity after the initiation of a Seismic
Electric Signal activity until the main shock: The behavior of seismicity in the area candidate to suffer a main shock is
investigated after the observation of the Seismic Electric Signal activity
until the impending mainshock. This makes use of the concept of natural time
$\chi$ and reveals that the probability density function of the variance
$\kappa_1(=< \chi^2 > -< \chi > ^2)$ exhibits distinct features before the
occurrence of the mainshock. Examples are presented, which refer to magnitude
class 6.0 earthquakes that occurred in Greece during the first two months in
2008. | cond-mat_stat-mech |
Critical dynamics of nonconserved $N$-vector model with anisotropic
nonequilibrium perturbations: We study dynamic field theories for nonconserving $N$-vector models that are
subject to spatial-anisotropic bias perturbations. We first investigate the
conditions under which these field theories can have a single length scale.
When N=2 or $N \ge 4$, it turns out that there are no such field theories, and,
hence, the corresponding models are pushed by the bias into the Ising class. We
further construct nontrivial field theories for N=3 case with certain bias
perturbations and analyze the renormalization-group flow equations. We find
that the three-component systems can exhibit rich critical behavior belonging
to two different universality classes. | cond-mat_stat-mech |
Single-vehicle data of highway traffic: microscopic description of
traffic phases: We present a detailed analysis of single-vehicle data which sheds some light
on the microscopic interaction of the vehicles. Besides the analysis of free
flow and synchronized traffic the data sets especially provide information
about wide jams which persist for a long time. The data have been collected at
a location far away from ramps and in the absence of speed limits which allows
a comparison with idealized traffic simulations. We also resolve some open
questions concerning the time-headway distribution. | cond-mat_stat-mech |
Coil-Globule transition of a single short polymer chain - an exact
enumeration study: We present an exact enumeration study of short SAWs in two as well as three
dimensions that addresses the question, `what is the shortest walk for which
the existence of all the three phases - coil, globule and the {\it theta} -
could be demonstrated'. Even though we could easily demonstrate the coil and
the globule phases from Free Energy considerations, we could demonstrate the
existence of a {\it theta} phase only by using a scaling form for the
distribution of gyration radius. That even such short walks have a scaling
behavior is an unexpected result of this work. | cond-mat_stat-mech |
How cooperatively folding are homopolymer molecular knots?: Detailed thermodynamic analysis of complex systems with multiple stable
configurational states allows for insight into the cooperativity of each
individual transition. In this work we derive a heat capacity decomposition
comprising contributions from each individual configurational state, which
together sum to a baseline heat capacity, and contributions from each
state-to-state transition. We apply this analysis framework to a series of
replica exchange molecular dynamics simulations of linear and 1-1
coarse-grained homo-oligomer models which fold into stable, configurationally
well-defined molecular knots, in order to better understand the parameters
leading to stable and cooperative folding of these knots. We find that a stiff
harmonic backbone bending angle potential is key to achieving knots with
specific 3D structures. Tuning the backbone equilibrium angle in small
increments yields a variety of knot topologies, including $3_1$, $5_1$, $7_1$,
and $8_{19}$ types. Populations of different knotted states as functions of
temperature can also be manipulated by tuning backbone torsion stiffness or by
adding side chain beads. We find that sharp total heat capacity peaks for the
homo-oligomer knots are largely due to a coil-to-globule transition, rather
than a cooperative knotting step. However, in some cases the cooperativity of
globule-to-knot and coil-to-globule transitions are comparable, suggesting that
highly cooperative folding to knotted structures can be achieved by refining
the model parameters or adding sequence specificity. | cond-mat_stat-mech |
Finite-time scaling for kinetic rough interfaces: We consider discrete models of kinetic rough interfaces that exhibit
space-time scale-invariance in height-height correlation. A generic scaling
theory implies that the dynamical structure factor of the height profile can
uniquely characterize the underlying dynamics. We provide a finite-time scaling
that systematically allows an estimation of the critical exponents and the
scaling functions, eventually establishing the universality class accurately.
As an illustration, we investigate a class of self-organized interface models
in random media with extremal dynamics. The isotropic version shows a faceted
pattern and belongs to the same universality class (as shown numerically) as
the Sneppen (model A). We also introduce an anisotropic version of the Sneppen
(model A) and suggest that the model belongs to the universality class of the
tensionless one-dimensional Kardar-Parisi-Zhang equation. | cond-mat_stat-mech |
Fermionic theory of nonequilibrium steady states: As the quantification of metabolism, nonequilibrium steady states play a
central role in living matter, but are beyond the purview of equilibrium
statistical mechanics. Here we develop a fermionic theory of nonequilibrium
steady states in continuous-time Markovian systems. The response to an
arbitrary perturbation is computed, and simplified in canonical cases. Beyond
response, we consider ensembles of NESS and derive a fluctuation-response
relation over a non-equilibrium ensemble. Some connections to quantum gravity
are pointed out, and the formulation is extended to a supersymmetric integral
one, which may form the basis of nontrivial solvable models of nonequilibrium
steady states. | cond-mat_stat-mech |
Phases fluctuations, self-similarity breaking and anomalous scalings in
driven nonequilibrium critical phenomena: We study in detail the dynamic scaling of the three-dimensional (3D) Ising
model driven through its critical point on finite-size lattices and show that a
series of new critical exponents are needed to account for the anomalous
scalings originating from breaking of self-similarity of the so-called phases
fluctuations. Our results demonstrate that new exponents are generally required
for scaling in the whole driven process once the lattice size or an externally
applied field are taken into account. These open a new door in critical
phenomena and suggest that much is yet to be explored in driven nonequilibrium
critical phenomena. | cond-mat_stat-mech |
Shearing of loose granular materials: A statistical mesoscopic model: A two-dimensional lattice model for the formation and evolution of shear
bands in granular media is proposed. Each lattice site is assigned a random
variable which reflects the local density. At every time step, the strain is
localized along a single shear-band which is a spanning path on the lattice
chosen through an extremum condition. The dynamics consists of randomly
changing the `density' of the sites only along the shear band, and then
repeating the procedure of locating the extremal path and changing it. Starting
from an initially uncorrelated density field, it is found that this dynamics
leads to a slow compaction along with a non-trivial patterning of the system,
with high density regions forming which shelter long-lived low-density valleys.
Further, as a result of these large density fluctuations, the shear band which
was initially equally likely to be found anywhere on the lattice, gets
progressively trapped for longer and longer periods of time. This state is
however meta-stable, and the system continues to evolve slowly in a manner
reminiscent of glassy dynamics. Several quantities have been studied
numerically which support this picture and elucidate the unusual system-size
effects at play. | cond-mat_stat-mech |
Understanding how both the partitions of a bipartite network affect its
one-mode projection: It is a well-known fact that the degree distribution (DD) of the nodes in a
partition of a bipartite network influences the DD of its one-mode projection
on that partition. However, there are no studies exploring the effect of the DD
of the other partition on the one-mode projection. In this article, we show
that the DD of the other partition, in fact, has a very strong influence on the
DD of the one-mode projection. We establish this fact by deriving the exact or
approximate closed-forms of the DD of the one-mode projection through the
application of generating function formalism followed by the method of
iterative convolution. The results are cross-validated through appropriate
simulations. | cond-mat_stat-mech |
Phase-ordering dynamics in itinerant quantum ferromagnets: The phase-ordering dynamics that result from domain coarsening are considered
for itinerant quantum ferromagnets. The fluctuation effects that invalidate the
Hertz theory of the quantum phase transition also affect the phase ordering.
For a quench into the ordered phase a transient regime appears, where the
domain growth follows a different power law than in the classical case, and for
asymptotically long times the prefactor of the t^{1/2} growth law has an
anomalous magnetization dependence. A quench to the quantum critical point
results in a growth law that is not a power-law function of time. Both
phenomenological scaling arguments and renormalization-group arguments are
given to derive these results, and estimates of experimentally relevant length
and time scales are presented. | cond-mat_stat-mech |
A detailed investigation into near degenerate exponential random graphs: The exponential family of random graphs has been a topic of continued
research interest. Despite the relative simplicity, these models capture a
variety of interesting features displayed by large-scale networks and allow us
to better understand how phases transition between one another as tuning
parameters vary. As the parameters cross certain lines, the model
asymptotically transitions from a very sparse graph to a very dense graph,
completely skipping all intermediate structures. We delve deeper into this near
degenerate tendency and give an explicit characterization of the asymptotic
graph structure as a function of the parameters. | cond-mat_stat-mech |
Entropy Production of Open Quantum System in Multi-Bath Environment: We study the entropy production of an open quantum system surrounded by a
complex environment consisting of several heat baths at different temperatures.
The detailed balance is elaborated in view of the distinguishable channels
provided by the couplings to different heat baths, and a refined entropy
production rate is derived accordingly. It is demonstrated that the entropy
production rates can characterize the quantum statistical property of the
baths: the bosonic and fermionic baths display different behaviors in the
high-temperature limit while they have the same asymptotic behavior at low
temperature. | cond-mat_stat-mech |
Jamming and pattern formation in models of segregation: We investigate the Schelling model of social segregation, formulated as an
intrinsically non-equilibrium system, in which the agents occupy districts (or
patches) rather than sites on a grid. We show that this allows the equations
governing the dynamical behaviour of the model to be derived. Analysis of these
equations reveals a jamming transition in the regime of low-vacancy density,
and inclusion of a spatial dimension in the model leads to a pattern forming
instability. Both of these phenomena exhibit unusual characteristics which may
be studied through our approach. | cond-mat_stat-mech |
Exploration of Order in Chaos with Replica Exchange Monte Carlo: A method for exploring unstable structures generated by nonlinear dynamical
systems is introduced. It is based on the sampling of initial conditions and
parameters by Replica Exchange Monte Carlo (REM), and efficient both for the
search of rare initial conditions and for the combined search of rare initial
conditions and parameters. Examples discussed here include the sampling of
unstable periodic orbits in chaos and search for the stable manifold of
unstable fixed points, as well as construction of the global bifurcation
diagram of a map. | cond-mat_stat-mech |
Nanoswimmers in a ratchet potential: Effects of a transverse rocking
force: We study the dynamics of a chemical nanoswimmer in a ratchet potential, which
is periodically rocked in the transverse direction. As a result of the
mechanochemical coupling, the self-propulsion velocity becomes force-dependent
and particle trajectories are rectified in the direction of the ratchet
modulation. The magnitude and direction of the nanoswimmer mean velocity depend
upon both the rocking amplitude and the frequency. Remarkably, for frequencies
larger than the inverse correlation time of the rotational diffusion, the
velocity exhibits oscillatory behaviour as a function of the amplitude and the
frequency with multiple reversals of the sign. These findings suggest that
mechanochemical coupling can be utilized for controlling the motion of
chemically active particles at the nanoscale. | cond-mat_stat-mech |
Detecting fuzzy community structures in complex networks with a Potts
model: A fast community detection algorithm based on a q-state Potts model is
presented. Communities in networks (groups of densely interconnected nodes that
are only loosely connected to the rest of the network) are found to coincide
with the domains of equal spin value in the minima of a modified Potts spin
glass Hamiltonian. Comparing global and local minima of the Hamiltonian allows
for the detection of overlapping (``fuzzy'') communities and quantifying the
association of nodes to multiple communities as well as the robustness of a
community. No prior knowledge of the number of communities has to be assumed. | cond-mat_stat-mech |
Ultracold Fermion Cooling Cycle using Heteronuclear Feshbach Resonances: We consider an ideal gas of Bose and Fermi atoms in a harmonic trap, with a
Feshbach resonance in the interspecies atomic scattering that can lead to
formation of fermionic molecules. We map out the phase diagram for this
three-component mixture in chemical and thermal equilibrium. Considering
adiabatic association and dissociation of the molecules, we identify a possible
cooling cycle, which in ideal circumstances can yield an exponential increase
of the phase-space density. | cond-mat_stat-mech |
Low self-affine exponents of fracture surfaces of glass ceramics: The geometry of post mortem rough fracture surfaces of porous glass ceramics
made of sintered glass beads is shown experimentally to be self-affine with an
exponent zeta=0.40 (0.04) remarkably lower than the 'universal' value zeta=0.8
frequently measured for many materials. This low value of zeta is similar to
that found for sandstone samples of similar micro structure and is also
practically independent on the porosity phi in the range investigated (3% < phi
< 26%) as well as on the bead diameter d and of the crack growth velocity. In
contrast, the roughness amplitude normalized by d increases linearly with phi
while it is still independent, within experimental error, of d and of the crack
propagation velocity. An interpretation of this variation is suggested in terms
of a transition from transgranular to intergranular fracture propagation with
no influence, however, on the exponent zeta. | cond-mat_stat-mech |
Glassy behavior of the site frustrated percolation model: The dynamical properties of the site frustrated percolation model are
investigated and compared with those of glass forming liquids. When the density
of the particles on the lattice becomes high enough, the dynamics of the model
becomes very slow, due to geometrical constraints, and rearrangement on large
scales is needed to allow relaxation. The autocorrelation functions, the
specific volume for different cooling rates, and the mean square displacement
are evaluated, and are found to exhibit glassy behavior. | cond-mat_stat-mech |
Variational HFB Equations in the Thomas-Fermi Limit for Ultracold
Trapped Gases: We derive variationally the HFB equations for a trapped self-interacting Bose
gas at finite temperature. In the Thomas-Fermi limit, we obtain simple
expressions for the condensate, the non condensate and the anomalous densities.
Their behavior in terms of the condensate fraction meets qualitatively the
experimental data. In particular, the non condensate and the anomalous
densities are peaked at the center of the trap and not at the edges as
predicted by the self-consistent HFB calculations. | cond-mat_stat-mech |
Parameters of state in the global thermodynamics of binary ideal gas
mixtures in a stationary heat flow: We formulate the first law of global thermodynamics for stationary states of
the binary ideal gas mixture subjected to heat flow. We map the non-uniform
system onto the uniform one and show that the internal energy
$U(S^*,V,N_1,N_2,f_1^*,f_2^*)$ is the function of the following parameters of
state: a non-equilibrium entropy $S^*$, volume $V$, number of particles of the
first component, $N_1$, number of particles of the second component $N_2$ and
the renormalized degrees of freedom. The parameters $f_1^*,f_2^*$, $N_1, N_2$
satisfy the relation $x_1f_1^*/f_1+x_2f_2^*/f_2=1$ ($f_1$, where $x_i$ is the
fraction of $i$ component, and $f_2$ are the degrees of freedom for each
component respectively). Thus only 5 parameters of state describe the
non-equilibrium state of the binary mixture in the heat flow. We calculate the
non-equilibrium entropy $S^{*}$ and new thermodynamic parameters of state
$f_1^*, f_2^*$ explicitly. The latter are responsible for heat generation due
to the concentration gradients. The theory reduces to equilibrium
thermodynamics, when the heat flux goes to zero. As in equilibrium
thermodynamics, the steady-state fundamental equation also leads to the
thermodynamic Maxwell relations for measurable steady-state properties. | cond-mat_stat-mech |
Single-particle excitations and the order parameter for a trapped
superfluid Fermi gas: We reveal a strong influence of a superfluid phase transition on the
character of single-particle excitations of a trapped neutral-atom Fermi gas.
Below the transition temperature the presence of a spatially inhomogeneous
order parameter (gap) shifts up the excitation eigenenergies and leads to the
appearance of in-gap excitations localized in the outer part of the gas sample.
The eigenenergies become sensitive to the gas temperature and are no longer
multiples of the trap frequencies. These features should manifest themselves in
a strong change of the density oscillations induced by modulations of the trap
frequencies and can be used for identifying the superfluid phase transition. | cond-mat_stat-mech |
Pricing Derivatives by Path Integral and Neural Networks: Recent progress in the development of efficient computational algorithms to
price financial derivatives is summarized. A first algorithm is based on a path
integral approach to option pricing, while a second algorithm makes use of a
neural network parameterization of option prices. The accuracy of the two
methods is established from comparisons with the results of the standard
procedures used in quantitative finance. | cond-mat_stat-mech |
Relativistic Nonextensive Thermodynamics: Starting from the basic prescriptions of the Tsallis' nonextensive
thermostatistics, i.e. generalized entropy and normalized q-expectation values,
we study the relativistic nonextensive thermodynamics and derive a Boltzmann
transport equation that implies the validity of the H-theorem where a local
nonextensive four-entropy density is considered. Macroscopic thermodynamic
functions and the equation of state for a perfect gas are derived at the
equilibrium. | cond-mat_stat-mech |
Coulomb Systems with Ideal Dielectric Boundaries: Free Fermion Point and
Universality: A two-component Coulomb gas confined by walls made of ideal dielectric
material is considered. In two dimensions at the special inverse temperature
$\beta = 2$, by using the Pfaffian method, the system is mapped onto a
four-component Fermi field theory with specific boundary conditions. The exact
solution is presented for a semi-infinite geometry of the dielectric wall (the
density profiles, the correlation functions) and for the strip geometry (the
surface tension, a finite-size correction of the grand potential). The
universal finite-size correction of the grand potential is shown to be a
consequence of the good screening properties, and its generalization is derived
for the conducting Coulomb gas confined in a slab of arbitrary dimension $\ge
2$ at any temperature. | cond-mat_stat-mech |
The Magnetic Eden Model: In the magnetic Eden model (MEM), particles have a spin and grow in contact
with a thermal bath. Although Ising-like interactions affect the growth
dynamics, deposited spins are frozen and not allowed to flip. This review
article focuses on recent developments and future prospects, such as
spontaneous switching phenomena, critical behavior associated with fractal,
wetting, and order-disorder phase transitions, the equilibrium/nonequilibrium
correspondence conjecture, as well as dynamical and critical features of the
MEM defined on complex network substrates. | cond-mat_stat-mech |
Constructing effective free energies for dynamical quantum phase
transitions in the transverse-field Ising chain: The theory of dynamical quantum phase transitions represents an attempt to
extend the concept of phase transitions to the far from equilibrium regime.
While there are many formal analogies to conventional transitions, it is a
major question to which extent it is possible to formulate a nonequilibrium
counterpart to a Landau-Ginzburg theory. In this work we take a first step in
this direction by constructing an effective free energy for continuous
dynamical quantum phase transitions appearing after quantum quenches in the
transverse-field Ising chain. Due to unitarity of quantum time evolution this
effective free energy becomes a complex quantity transforming the conventional
minimization principle of the free energy into a saddle-point equation in the
complex plane of the order parameter, which as in equilibrium is the
magnetization. We study this effective free energy in the vicinity of the
dynamical quantum phase transition by performing an expansion in terms of the
complex magnetization and discuss the connections to the equilibrium case.
Furthermore, we study the influence of perturbations and signatures of these
dynamical quantum phase transitions in spin correlation functions. | cond-mat_stat-mech |
Symmetries and zero modes in sample path large deviations: Sharp large deviation estimates for stochastic differential equations with
small noise, based on minimizing the Freidlin-Wentzell action functional under
appropriate boundary conditions, can be obtained by integrating certain matrix
Riccati differential equations along the large deviation minimizers or
instantons, either forward or backward in time. Previous works in this
direction often rely on the existence of isolated minimizers with positive
definite second variation. By adopting techniques from field theory and
explicitly evaluating the large deviation prefactors as functional determinant
ratios using Forman's theorem, we extend the approach to general systems where
degenerate submanifolds of minimizers exist. The key technique for this is a
boundary-type regularization of the second variation operator. This extension
is particularly relevant if the system possesses continuous symmetries that are
broken by the instantons. We find that removing the vanishing eigenvalues
associated with the zero modes is possible within the Riccati formulation and
amounts to modifying the initial or final conditions and evaluation of the
Riccati matrices. We apply our results in multiple examples including a
dynamical phase transition for the average surface height in short-time large
deviations of the one-dimensional Kardar-Parisi-Zhang equation with flat
initial profile. | cond-mat_stat-mech |
On the spatially periodic ordering in the system of electrons above the
surface of liquid helium in an external electric field: A theory of equilibrium states of electrons above a liquid helium surface in
the presence of an external clamping field is built based on the first
principles of quantum statistics for the system of many identical
Fermi-particles. The approach is based on the variation principle modified for
the considered system and on Thomas-Fermi model. In terms of the developed
theory we obtain the self-consistency equations that connect the parameters of
the system description, i.e., the potential of a static electric field, the
distribution function of electrons and the surface profile of a liquid
dielectric. The equations are used to study the phase transition of the system
to a spatially periodic state. To demonstrate the capabilities of the proposed
method, the characteristics of the phase transition of the system to a
spatially periodic state of a trough type are analyzed. | cond-mat_stat-mech |
Random Matrix Theory approach to Mesoscopic Fluctuations of Heat Current: We consider an ensemble of fully connected networks of N oscillators coupled
harmonically with random springs and show, using Random Matrix Theory
considerations, that both the average phonon heat current and its variance are
scale-invariant and take universal values in the large N-limit. These anomalous
mesoscopic uctuations is the hallmark of strong correlations between normal
modes. | cond-mat_stat-mech |
Asymptotic Dynamics of Breathers in Fermi-Pasta-Ulam Chains: We study the asymptotic dynamics of breathers in finite Fermi-Pasta-Ulam
chains at zero and non-zero temperatures. While such breathers are essentially
stationary and very long-lived at zero temperature, thermal fluctuations tend
to lead to breather motion and more rapid decay. | cond-mat_stat-mech |
Active XY model on a substrate: Density fluctuations and phase ordering: We explore the generic long wavelength properties of an active XY model on a
substrate, consisting of collection of nearly phase-ordered active XY spins in
contact with a diffusing, conserved species, as a representative system of
active spinners with a conservation law. The spins rotate actively in response
to the local density fluctuations and local phase differences, on a solid
substrate. We investigate this system by Monte-Carlo simulations of an
agent-based model, which we set up, complemented by the hydrodynamic theory for
the system. We demonstrate that this system can phase-synchronize without any
hydrodynamic interactions. Our combined numerical and analytical studies show
that this model, when stable, displays hitherto unstudied scaling behavior: As
a consequence of the interplay between the mobility, active rotation and number
conservation, such a system can be stable over a wide range of the model
parameters characterized by a novel correspondence between the phase and
density fluctuations. In different regions of the phase space where the
phase-ordered system is stable, it shows phase ordering which is generically
either logarithmically stronger than the conventional quasi long range order
(QLRO) found in its equilibrium limit, together with "miniscule number
fluctuations", or logarithmically weaker than QLRO along with "giant number
fluctuations", showing a novel one-to-one correspondence between phase ordering
and density fluctuations in the ordered states. Intriguingly, these scaling
exponents are found to depend explicitly on the model parameters. We further
show that in other parameter regimes there are no stable, ordered phases.
Instead, two distinct types of disordered states with short range phase-order
are found, characterized by the presence or absence of stable clusters of
finite sizes. | cond-mat_stat-mech |
Ballistic spin transport in a periodically driven integrable quantum
system: We demonstrate ballistic spin transport of an integrable unitary quantum
circuit, which can be understood either as a paradigm of an integrable
periodically driven (Floquet) spin chain, or as a Trotterized anisotropic
($XXZ$) Heisenberg spin-1/2 model. We construct an analytic family of
quasi-local conservation laws that break the spin-reversal symmetry and compute
a lower bound on the spin Drude weight which is found to be a fractal function
of the anisotropy parameter. Extensive numerical simulations of spin transport
suggest that this fractal lower bound is in fact tight. | cond-mat_stat-mech |
Collision densities and mean residence times for $d$-dimensional
exponential flights: In this paper we analyze some aspects of {\em exponential flights}, a
stochastic process that governs the evolution of many random transport
phenomena, such as neutron propagation, chemical/biological species migration,
or electron motion. We introduce a general framework for $d$-dimensional
setups, and emphasize that exponential flights represent a deceivingly simple
system, where in most cases closed-form formulas can hardly be obtained. We
derive a number of novel exact (where possible) or asymptotic results, among
which the stationary probability density for 2d systems, a long-standing issue
in Physics, and the mean residence time in a given volume. Bounded or
unbounded, as well as scattering or absorbing domains are examined, and Monte
Carlo simulations are performed so as to support our findings. | cond-mat_stat-mech |
A Simple Model of Superconducting Vortex Avalanches: We introduce a simple lattice model of superconducting vortices driven by
repulsive interactions through a random pinning potential. The model describes
the behavior at the scale of the London length lambda or larger. It
self-organizes to a critical state, characterized by a constant flux density
gradient, where the activity takes place in terms of avalanches spanning all
length scales up to the system size. We determine scaling relations as well as
four universal critical exponents for avalanche moments and durations: tau =
1.63 +/- 0.02, D = 2.7 +/- 0.1, z = 1.5 +/- 0.1, and tau_t = 2.13 +/- 0.14, for
the system driven at the boundary. | cond-mat_stat-mech |
Information Geometry, Phase Transitions, and Widom Lines : Magnetic and
Liquid Systems: We study information geometry of the thermodynamics of first and second order
phase transitions, and beyond criticality, in magnetic and liquid systems. We
establish a universal microscopic characterization of such phase transitions
via the equality of correlation lengths $\xi$ in coexisting phases, where $\xi$
is related to the scalar curvature of the equilibrium thermodynamic state
space. The 1-D Ising model, and the mean-field Curie-Weiss model are discussed,
and we show that information geometry correctly describes the phase behavior
for the latter. The Widom lines for these systems are also established. We
further study a simple model for the thermodynamics of liquid-liquid phase
co-existence, and show that our method provides a simple and direct way to
obtain its phase behavior and the locations of the Widom lines. Our analysis
points towards multiple Widom lines in liquid systems. | cond-mat_stat-mech |
Entanglement in Far From Equilibrium Stationary States: We present four estimators of the entanglement (or interdepency) of
ground-states in which the coefficients are all real nonnegative and therefore
can be interpreted as probabilities of configurations. Such ground-states of
hermitian and non-hermitian Hamiltonians can be given, for example, by
superpositions of valence bond states which can describe equilibrium but also
stationary states of stochastic models. We consider in detail the last case.
Using analytical and numerical methods we compare the values of the estimators
in the directed polymer and the raise and peel models which have massive,
conformal invariant and non-conformal invariant massless phases. We show that
like in the case of the quantum problem, the estimators verify the area law and
can therefore be used to signal phase transitions in stationary states. | cond-mat_stat-mech |
Rejoinder to the Response arXiv:0812.2330 to 'Comment on a recent
conjectured solution of the three-dimensional Ising model': We comment on Z. D. Zhang's Response [arXiv:0812.2330] to our recent Comment
[arXiv:0811.3876] addressing the conjectured solution of the three-dimensional
Ising model reported in [arXiv:0705.1045]. | cond-mat_stat-mech |
Injected Power Fluctuations in 1D Dissipative Systems: Using fermionic techniques, we compute exactly the large deviation function
(ldf) of the time-integrated injected power in several one-dimensional
dissipative systems of classical spins. The dynamics are T=0 Glauber dynamics
supplemented by an injection mechanism, which is taken as a Poissonian flipping
of one particular spin. We discuss the physical content of the results,
specifically the influence of the rate of the Poisson process on the properties
of the ldf. | cond-mat_stat-mech |
Vertex dynamics during domain growth in three-state models: Topological aspects of interfaces are studied by comparing quantitatively the
evolving three-color patterns in three different models, such as the
three-state voter, Potts and extended voter models. The statistical analysis of
some geometrical features allows to explore the role of different elementary
processes during distinct coarsening phenomena in the above models. | cond-mat_stat-mech |
Phase transition of $q$-state clock models on heptagonal lattices: We study the $q$-state clock models on heptagonal lattices assigned on a
negatively curved surface. We show that the system exhibits three classes of
equilibrium phases; in between ordered and disordered phases, an intermediate
phase characterized by a diverging susceptibility with no magnetic order is
observed at every $q \ge 2$. The persistence of the third phase for all $q$ is
in contrast with the disappearance of the counterpart phase in a planar system
for small $q$, which indicates the significance of nonvanishing surface-volume
ratio that is peculiar in the heptagonal lattice. Analytic arguments based on
Ginzburg-Landau theory and generalized Cayley trees make clear that the
two-stage transition in the present system is attributed to an energy gap of
spin-wave excitations and strong boundary-spin contributions. We further
demonstrate that boundary effects breaks the mean-field character in the bulk
region, which establishes the consistency with results of clock models on
boundary-free hyperbolic lattices. | cond-mat_stat-mech |
Phase diagram of S=1/2 XXZ chain with NNN interaction: We study the ground state properties of one-dimensional XXZ model with
next-nearest neighbor coupling alpha and anisotropy Delta. We find the direct
transition between the ferromagnetic phase and the spontaneously dimerized
phase. This is surprising, because the ferromagnetic phase is classical,
whereas the dimer phase is a purely quantum and nonmagnetic phase. We also
discuss the effect of bond alternation which arises in realistic systems due to
lattice distortion. Our results mean that the direct transition between the
ferromagnetic and spin-Peierls phase occur. | cond-mat_stat-mech |
Efficiency of autonomous soft nano-machines at maximum power: We consider nano-sized artificial or biological machines working in steady
state enforced by imposing non-equilibrium concentrations of solutes or by
applying external forces, torques or electric fields. For unicyclic and
strongly coupled multicyclic machines, efficiency at maximum power is not
bounded by the linear response value 1/2. For strong driving, it can even
approach the thermodynamic limit 1. Quite generally, such machines fall in
three different classes characterized, respectively, as "strong and efficient",
"strong and inefficient", and "balanced". For weakly coupled multicyclic
machines, efficiency at maximum power has lost any universality even in the
linear response regime. | cond-mat_stat-mech |
Finite Size Effect on Bose-Einstein Condensation: We show various aspects of finite size effects on Bose-Einstein
condensation(BEC). In the first section we introduce very briefly the BEC of
harmonically trapped ideal Bose gas. In the second section we theoretically
argued that Bose-Einstein(B-E) statistics needs a correction for finite system
at ultralow temperatures. As a corrected statistics we introduced a Tsallis
type of generalized B-E statistics. The condensate fraction calculated with
this generalized B-E statistics, is satisfied well with the experimental
result. In the third section we show how to apply the scaling theory in an
inhomogeneous system like harmonically trapped Bose condensate at finite
temperatures. We calculate the temperature dependence of the critical number of
particles by a scaling theory within the Hartree-Fock approximation and find
that there is a dramatic increase in the critical number of particles as the
condensation point is approached. Our results support the experimental result
which was obtained well below the condensation temperature. In the fourth
section we concentrate on the thermodynamic Casimir force on the Bose-Einstein
condensate. We explored the temperature dependence of the Casimir force. | cond-mat_stat-mech |
Phase diagram of two-lane driven diffusive systems: We consider a large class of two-lane driven diffusive systems in contact
with reservoirs at their boundaries and develop a stability analysis as a
method to derive the phase diagrams of such systems. We illustrate the method
by deriving phase diagrams for the asymmetric exclusion process coupled to
various second lanes: a diffusive lane; an asymmetric exclusion process with
advection in the same direction as the first lane, and an asymmetric exclusion
process with advection in the opposite direction. The competing currents on the
two lanes naturally lead to a very rich phenomenology and we find a variety of
phase diagrams. It is shown that the stability analysis is equivalent to an
`extremal current principle' for the total current in the two lanes. We also
point to classes of models where both the stability analysis and the extremal
current principle fail. | cond-mat_stat-mech |
Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet: Ordering of the classical Heisenberg antiferromagnet on the triangular
lattice is studied by means of a mean-field calculation, a scaling argument and
a Monte Carlo simulation, with special attention to its vortex degree of
freedom. The model exhibits a thermodynamic transition driven by the Z_2-vortex
binding-unbinding, at which various thermodynamic quantities exhibit an
essential singularity. The low-temperature state is a "spin-gel" state with a
long but finite spin correlation length where the ergodicity is broken
topologically. Implications to recent experiments on triangular-lattice
Heisenberg antiferromagnets are discussed. | cond-mat_stat-mech |
Complementary aspects of non-equilibrium thermodynamics: Bio-molecules are active agents in that they consume energy to perform tasks.
The standard theoretical description, however, considers only a system-external
work agent. Fluctuation theorems, for example, do not allow work-exchange
between fluctuating molecules. This tradition leaves `action through work', an
essential characteristic of an active agent, out of proper thermodynamic
consideration. Here, we investigate thermodynamics that considers
internal-work. We find a complementary set of relations that capture the
production of free energy in molecular interactions while obeying the second
law of thermodynamics. This thermodynamic description is in stark contrast to
the traditional one. A choice of an axiom whether one treats a portion of
Hamiltonian as `internal-work' or `internal-energy' decides which of the two
complementary descriptions manifests among the dual. We illustrate, by
examining an allosteric transition and a single-molecule
fluorescence-resonance-energy-transfer measurement of proteins, that the
complementary set is useful in identifying work content by experimental and
numerical observation. | cond-mat_stat-mech |
Complex-valued second difference as a measure of stabilization of
complex dissipative statistical systems: Girko ensemble: A quantum statistical system with energy dissipation is studied. Its
statistics is governed by random complex-valued non-Hermitean Hamiltonians
belonging to complex Ginibre ensemble. The eigenenergies are shown to form
stable structure. Analogy of Wigner and Dyson with system of electrical charges
is drawn. | cond-mat_stat-mech |
Master equation approach to the stochastic accumulation dynamics of
bacterial cell cycle: The mechanism of bacterial cell size control has been a mystery for decades,
which involves the well-coordinated growth and division in the cell cycle. The
revolutionary modern techniques of microfluidics and the advanced live imaging
analysis techniques allow long term observations and high-throughput analysis
of bacterial growth on single cell level, promoting a new wave of quantitative
investigations on this puzzle. Taking the opportunity, this theoretical study
aims to clarify the stochastic nature of bacterial cell size control under the
assumption of the accumulation mechanism, which is favoured by recent
experiments on species of bacteria. Via the master equation approach with
properly chosen boundary conditions, the distributions concerned in cell size
control are estimated and are confirmed by experiments. In this analysis, the
inter-generation Green's function is analytically evaluated as the key to
bridge two kinds of statistics used in batch-culture and mother machine
experiments. This framework allows us to quantify the noise level in growth and
accumulation according to experimental data. As a consequence of non-Gaussian
noises of the added sizes, the non-equilibrium nature of bacterial cell size
homeostasis is predicted, of which the biological meaning requires further
investigation. | cond-mat_stat-mech |
Occupation times on a comb with ramified teeth: We investigate occupation time statistics for random walks on a comb with
ramified teeth. This is achieved through the relation between the occupation
time and the first passage times. Statistics of occupation times in half space
follows Lamperti's distribution, i.e. the generalized arcsine law holds.
Transitions between different behaviors are observed, which are controlled by
the size of the backbone and teeth of the comb, as well as bias. Occupation
time on a non-simply connected domain is analyzed with a mean-field theory and
numerical simulations. In that case, the generalized arcsine law isn't valid. | cond-mat_stat-mech |
Firms Growth Dynamics, Competition and Power Law Scaling: We study the growth dynamics of the size of manufacturing firms considering
competition and normal distribution of competency. We start with the fact that
all components of the system struggle with each other for growth as happened in
real competitive bussiness world. The detailed quantitative agreement of the
theory with empirical results of firms growth based on a large economic
database spanning over 20 years is good .Further we find that this basic law of
competition leads approximately a power law scaling over a wide range of
parameters. The empirical datas are in accordance with present theory rather
than a simple power law. | cond-mat_stat-mech |
Self-Similar Factor Approximants: The problem of reconstructing functions from their asymptotic expansions in
powers of a small variable is addressed by deriving a novel type of
approximants. The derivation is based on the self-similar approximation theory,
which presents the passage from one approximant to another as the motion
realized by a dynamical system with the property of group self-similarity. The
derived approximants, because of their form, are named the self-similar factor
approximants. These complement the obtained earlier self-similar exponential
approximants and self-similar root approximants. The specific feature of the
self-similar factor approximants is that their control functions, providing
convergence of the computational algorithm, are completely defined from the
accuracy-through-order conditions. These approximants contain the Pade
approximants as a particular case, and in some limit they can be reduced to the
self-similar exponential approximants previously introduced by two of us. It is
proved that the self-similar factor approximants are able to reproduce exactly
a wide class of functions which include a variety of transcendental functions.
For other functions, not pertaining to this exactly reproducible class, the
factor approximants provide very accurate approximations, whose accuracy
surpasses significantly that of the most accurate Pade approximants. This is
illustrated by a number of examples showing the generality and accuracy of the
factor approximants even when conventional techniques meet serious
difficulties. | cond-mat_stat-mech |
Numerical validation of the Complex Swift-Hohenberg equation for lasers: Order parameter equations, such as the complex Swift-Hohenberg (CSH)
equation, offer a simplified and universal description that hold close to an
instability threshold. The universality of the description refers to the fact
that the same kind of instability produces the same order parameter equation.
In the case of lasers, the instability usually corresponds to the emitting
threshold, and the CSH equation can be obtained from the Maxwell-Bloch (MB)
equations for a class C laser with small detuning. In this paper we numerically
check the validity of the CSH equation as an approximation of the MB equations,
taking into account that its terms are of different asymptotic order, and that,
despite of having been systematically overlooked in the literature, this fact
is essential in order to correctly capture the weakly nonlinear dynamics of the
MB. The approximate distance to threshold range for which the CSH equation
holds is also estimated. | cond-mat_stat-mech |
Improved Lower Bounds on the Ground-State Entropy of the
Antiferromagnetic Potts Model: We present generalized methods for calculating lower bounds on the
ground-state entropy per site, $S_0$, or equivalently, the ground-state
degeneracy per site, $W=e^{S_0/k_B}$, of the antiferromagnetic Potts model. We
use these methods to derive improved lower bounds on $W$ for several lattices. | cond-mat_stat-mech |
Thermal buckling and symmetry breaking in thin ribbons under compression: Understanding thin sheets, ranging from the macro to the nanoscale, can allow
control of mechanical properties such as deformability. Out-of-plane buckling
due to in-plane compression can be a key feature in designing new materials.
While thin-plate theory can predict critical buckling thresholds for thin
frames and nanoribbons at very low temperatures, a unifying framework to
describe the effects of thermal fluctuations on buckling at more elevated
temperatures presents subtle difficulties. We develop and test a theoretical
approach that includes both an in-plane compression and an out-of-plane
perturbing field to describe the mechanics of thermalised ribbons above and
below the buckling transition. We show that, once the elastic constants are
renormalised to take into account the ribbon's width (in units of the thermal
length scale), we can map the physics onto a mean-field treatment of buckling,
provided the length is short compared to a ribbon persistence length. Our
theoretical predictions are checked by extensive molecular dynamics simulations
of thin thermalised ribbons under axial compression. | cond-mat_stat-mech |
Accuracy and Efficiency of Simplified Tensor Network Codes: We examine in detail the accuracy, efficiency and implementation issues that
arise when a simplified code structure is employed to evaluate the partition
function of the two-dimensional square Ising model on periodic lattices though
repeated tensor contractions. | cond-mat_stat-mech |
Nontrivial critical crossover between directed percolation models:
Effect of infinitely many absorbing states: At non-equilibrium phase transitions into absorbing (trapped) states, it is
well known that the directed percolation (DP) critical scaling is shared by two
classes of models with a single (S) absorbing state and with infinitely many
(IM) absorbing states. We study the crossover behavior in one dimension,
arising from a considerable reduction of the number of absorbing states
(typically from the IM-type to the S-type DP models), by following two
different (excitatory or inhibitory) routes which make the auxiliary field
density abruptly jump at the crossover. Along the excitatory route, the system
becomes overly activated even for an infinitesimal perturbation and its
crossover becomes discontinuous. Along the inhibitory route, we find continuous
crossover with the universal crossover exponent $\phi\simeq 1.78(6)$, which is
argued to be equal to $\nu_\|$, the relaxation time exponent of the DP
universality class on a general footing. This conjecture is also confirmed in
the case of the directed Ising (parity-conserving) class. Finally, we discuss
the effect of diffusion to the IM-type models and suggest an argument why
diffusive models with some hybrid-type reactions should belong to the DP class. | cond-mat_stat-mech |
Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion
Process with Finite Resources: We revisit a totally asymmetric simple exclusion process (TASEP) with open
boundaries and a global constraint on the total number of particles [Adams, et.
al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles
into the lattice depends on the number available in the reservoir. Thus, the
total occupation on the lattice feeds back into its filling process. Although a
simple domain wall theory provided reasonably good predictions for Monte Carlo
simulation results for certain quantities, it did not account for the
fluctuations of this feedback. We generalize the previous study and find
dramatically improved predictions for, e.g., the density profile on the lattice
and provide a better understanding of the phenomenon of "shock localization." | cond-mat_stat-mech |
Spectral fingerprints of non-equilibrium dynamics: The case of a
Brownian gyrator: The same system can exhibit a completely different dynamical behavior when it
evolves in equilibrium conditions or when it is driven out-of-equilibrium by,
e.g., connecting some of its components to heat baths kept at different
temperatures. Here we concentrate on an analytically solvable and
experimentally-relevant model of such a system -- the so-called Brownian
gyrator -- a two-dimensional nanomachine that performs a systematic, on
average, rotation around the origin under non-equilibrium conditions, while no
net rotation takes place in equilibrium. On this example, we discuss a question
whether it is possible to distinguish between two types of a behavior judging
not upon the statistical properties of the trajectories of components, but
rather upon their respective spectral densities. The latter are widely used to
characterize diverse dynamical systems and are routinely calculated from the
data using standard built-in packages. From such a perspective, we inquire
whether the power spectral densities possess some "fingerprint" properties
specific to the behavior in non-equilibrium. We show that indeed one can
conclusively distinguish between equilibrium and non-equilibrium dynamics by
analyzing the cross-correlations between the spectral densities of both
components in the short frequency limit, or from the spectral densities of both
components evaluated at zero frequency. Our analytical predictions,
corroborated by experimental and numerical results, open a new direction for
the analysis of a non-equilibrium dynamics. | cond-mat_stat-mech |
Effects of node position on diffusion and trapping efficiency for random
walks on fractal scale-free trees: We study unbiased discrete random walks on the FSFT based on the its
self-similar structure and the relations between random walks and electrical
networks. First, we provide new methods to derive analytic solutions of the
MFPT for any pair of nodes, the MTT for any target node and MDT for any
starting node. And then, using the MTT and the MDT as the measures of trapping
efficiency and diffusion efficiency respectively, we analyze the effect of
trap's position on trapping efficiency and the effect of starting position on
diffusion efficiency. Comparing the trapping efficiency and diffusion
efficiency among all nodes of FSFT, we find the best (or worst) trapping sites
and the best (or worst) diffusing sites. Our results show that: the node which
is at the center of FSFT is the best trapping site, but it is also the worst
diffusing site. The nodes which are the farthest nodes from the two hubs are
the worst trapping sites, but they are also the best diffusion sites. Comparing
the maximum and minimum of MTT and MDT, we found that the maximum of MTT is
almost $\frac{20m^2+32m+12}{4m^2+4m+1}$ times of the minimum of MTT, but the
the maximum of MDT is almost equal to the minimum of MDT. These results shows
that the position of target node has big effect on trapping efficiency, but the
position of starting node almost has no effect on diffusion efficiency. We also
conducted numerical simulation to test the results we have derived, the results
we derived are consistent with those obtained by numerical simulation. | cond-mat_stat-mech |
Diffusive transport on networks with stochastic resetting to multiple
nodes: We study the diffusive transport of Markovian random walks on arbitrary
networks with stochastic resetting to multiple nodes. We deduce analytical
expressions for the stationary occupation probability and for the mean and
global first passage times. This general approach allows us to characterize the
effect of resetting on the capacity of random walk strategies to reach a
particular target or to explore the network. Our formalism holds for ergodic
random walks and can be implemented from the spectral properties of the random
walk without resetting, providing a tool to analyze the efficiency of search
strategies with resetting to multiple nodes. We apply the methods developed
here to the dynamics with two reset nodes and derive analytical results for
normal random walks and L\'evy flights on rings. We also explore the effect of
resetting to multiple nodes on a comb graph, L\'evy flights that visit specific
locations in a continuous space, and the Google random walk strategy on regular
networks. | cond-mat_stat-mech |
Path statistics, memory, and coarse-graining of continuous-time random
walks on networks: Continuous-time random walks (CTRWs) on discrete state spaces, ranging from
regular lattices to complex networks, are ubiquitous across physics, chemistry,
and biology. Models with coarse-grained states, for example those employed in
studies of molecular kinetics, and models with spatial disorder can give rise
to memory and non-exponential distributions of waiting times and first-passage
statistics. However, existing methods for analyzing CTRWs on complex energy
landscapes do not address these effects. We therefore use statistical mechanics
of the nonequilibrium path ensemble to characterize first-passage CTRWs on
networks with arbitrary connectivity, energy landscape, and waiting time
distributions. Our approach is valuable for calculating higher moments (beyond
the mean) of path length, time, and action, as well as statistics of any
conservative or non-conservative force along a path. For homogeneous networks
we derive exact relations between length and time moments, quantifying the
validity of approximating a continuous-time process with its discrete-time
projection. For more general models we obtain recursion relations, reminiscent
of transfer matrix and exact enumeration techniques, to efficiently calculate
path statistics numerically. We have implemented our algorithm in PathMAN, a
Python script that users can easily apply to their model of choice. We
demonstrate the algorithm on a few representative examples which underscore the
importance of non-exponential distributions, memory, and coarse-graining in
CTRWs. | cond-mat_stat-mech |
Dynamic Phase Transition in the Kinetic Spin-3/2 Blume-Capel Model:
Phase Diagrams in the Temperature and Crystal-Field Interaction Plane: We analyze, within a mean-field approach, the stationary states of the
kinetic spin-3/2 Blume-Capel model by the Glauber-type stochastic dynamics and
subject to a time-dependent oscillating external magnetic field. The dynamic
phase transition points are obtained by investigating the behavior of the
dynamic magnetization as a function of temperature and as well as calculating
the Liapunov exponent. Phase diagrams are constructed in the temperature and
crystal-field interaction plane. We find five fundamental types of phase
diagrams for the different values of the reduced magnetic field amplitude
parameter (h) in which they present a disordered, two ordered phases and the
coexistences phase regions. The phase diagrams also exhibit a dynamic double
critical end point for 0<h<1.44, one dynamic tricritical point for 1.44<h<5.06
and two dynamic tricritical points for h>5.06. | cond-mat_stat-mech |
Universal bridge functional for infinitely diluted solutions: a case
study for Lennard-Jones spheres of different diameter: In the paper we propose an universal bridge functional for the closure of the
Ornstein-Zernike (OZ) equation for the case of infinitely diluted solutions of
Lennard-Jones shperes of different size in the Lennard-Jones fluid. Bridge
functional is paprameterized using the data of the Molecular Dynamics (MD)
simulations. We show that for all investigated systems the bridge functional
can be efficiently papameterized with the exponential function which depends
only on the ratio of sizes of the solute and solvent atoms. To check the
parameterization we solve the OZ equation with the closure which includes the
parametrized functional and with the closure without the bridge functional
(Hyper-netted chain closure). We show that introducing the bridge functional
allows to obtain radial distribution functions (RDFs), which are close to the
MD results and essentially improve predictions of the location and height of
the first peak of the RDF. | cond-mat_stat-mech |
Dynamics of Ising models coupled microscopically to bath systems: Based on the Robertson theory the nonlinear dynamics of general Ising systems
coupled microscopically to bath systems is investigated leading to two
complimentary approaches. Within the master equation approach microscopically
founded transition rates are presented which essentially differ from the usual
phenological rates. The second approach leads to coupled equations of motion
for the local magnetizations and the exchange energy. Simple examples are
discussed and the general results are applied to the Sherrington-Kirkpatrick
spin glass model. | cond-mat_stat-mech |
Phase Transitions in a Forest-Fire Model: We investigate a forest-fire model with the density of empty sites as control
parameter. The model exhibits three phases, separated by one first-order phase
transition and one 'mixed' phase transition which shows critical behavior on
only one side and hysteresis. The critical behavior is found to be that of the
self-organized critical forest-fire model [B. Drossel and F. Schwabl, Phys.
Rev. Lett. 69, 1629 (1992)], whereas in the adjacent phase one finds the spiral
waves of the Bak et al. forest-fire model [P. Bak, K. Chen and C. Tang, Phys.
Lett. A 147, 297 (1990)]. In the third phase one observes clustering of trees
with the fire burning at the edges of the clusters. The relation between the
density distribution in the spiral state and the percolation threshold is
explained and the implications for stationary states with spiral waves in
arbitrary excitable systems are discussed. Furthermore, we comment on the
possibility of mapping self-organized critical systems onto 'ordinary' critical
systems. | cond-mat_stat-mech |
Renewal equations for single-particle diffusion through a semipermeable
interface: Diffusion through semipermeable interfaces has a wide range of applications,
ranging from molecular transport through biological membranes to reverse
osmosis for water purification using artificial membranes. At the
single-particle level, one-dimensional diffusion through a barrier with
constant permeability $\kappa_0$ can be modeled in terms of so-called snapping
out Brownian motion (BM). The latter sews together successive rounds of
partially reflecting BMs that are restricted to either the left or right of the
barrier. Each round is killed (absorbed) at the barrier when its Brownian local
time exceeds an exponential random variable parameterized by $\kappa_0$. A new
round is then immediately started in either direction with equal probability.
It has recently been shown that the probability density for snapping out BM
satisfies a renewal equation that relates the full density to the probability
densities of partially reflected BM on either side of the barrier. Moreover,
generalized versions of the renewal equation can be constructed that
incorporate non-Markovian, encounter-based models of absorption. In this paper
we extend the renewal theory of snapping out BM to single-particle diffusion in
bounded domains and higher spatial dimensions. We also consider an example of
an asymmetric interface in which the directional switching after each
absorption event is biased. Finally, we show how to incorporate an
encounter-based model of absorption for single-particle diffusion through a
spherically symmetric interface. We find that, even when the same non-Markovian
model of absorption applies on either side of the interface, the resulting
permeability is an asymmetric time-dependent function with memory. Moreover,
the permeability functions tend to be heavy-tailed. | cond-mat_stat-mech |
Some universal trends of the Mie(n,m) fluid thermodynamics: By using canonical Monte Carlo simulation, the liquid-vapor phase diagram,
surface tension, interface width, and pressure for the Mie(n,m) model fluids
are calculated for six pairs of parameters $m$ and $n$. It is shown that after
certain re-scaling of fluid density the corresponding states rule can be
applied for the calculations of the thermodynamic properties of the Mie model
fluids, and for some real substances | cond-mat_stat-mech |
Innovative insights into which statements the third law of
thermodynamics includes exactly: It is found from textbooks and literature that the third law of
thermodynamics has three different statements, i.e., the Nernst theorem,
unattainability statement of absolute zero temperature, and heat capacity
statement. It is pointed out that such three statements correspond to three
thermodynamic parameters, which are, respectively, the entropy, temperature,
and heat capacity, and can be obtained by extrapolating the experimental
results of different parameters at ultra-low temperatures to absolute zero. It
is expounded that because there's no need for additional assumptions in the
derivation of the Nernst equation, the Nernst theorem should be renamed as the
Nernst statement. Moreover, it is proved that both the Nernst statement and the
heat capacity statement are mutually deducible and equivalent, while the
unattainability of absolute zero temperature is only a corollary of the Nernst
statement or the heat capacity statement so that it is unsuitably referred to
as one statement of the third law of thermodynamics. The conclusion is that the
Nernst statement and the heat capacity statement are two equivalent statements
of the third law of thermodynamics. | cond-mat_stat-mech |
Cardy states, defect lines and chiral operators of coset CFTs on the
lattice: We construct Cardy states, defect lines and chiral operators for rational
coset conformal field theories on the lattice. The bulk theory is obtained by
taking the overlap between tensor network representations of different
string-nets, while the primary fields emerge from using the topological
superselection sectors of the anyons in the original topological theory. This
mapping provides an explicit manifestation of the equivalence between conformal
field theories in two dimensions and topological field theories in three
dimensions: their groundstates and elementary excitations are represented by
exactly the same tensors. | cond-mat_stat-mech |
Random-cluster multi-histogram sampling for the q-state Potts model: Using the random-cluster representation of the $q$-state Potts models we
consider the pooling of data from cluster-update Monte Carlo simulations for
different thermal couplings $K$ and number of states per spin $q$. Proper
combination of histograms allows for the evaluation of thermal averages in a
broad range of $K$ and $q$ values, including non-integer values of $q$. Due to
restrictions in the sampling process proper normalization of the combined
histogram data is non-trivial. We discuss the different possibilities and
analyze their respective ranges of applicability. | cond-mat_stat-mech |
Properties of pattern formation and selection processes in
nonequilibrium systems with external fluctuations: We extend the phase field crystal method for nonequilibrium patterning to
stochastic systems with external source where transient dynamics is essential.
It was shown that at short time scales the system manifests pattern selection
processes. These processes are studied by means of the structure function
dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed by
means of numerical simulations. | cond-mat_stat-mech |
Coherent Averaging: an Alternative to the Average Hamiltonian Theory: Line-narrowing by periodic modulation of nuclear spin interaction
Hamiltonians is the central element of various experimental techniques in NMR
spectroscopy. In this study, we present a theoretical formulation of coherent
averaging to calculate the heights of narrowed spectral peaks. This concept is
experimentally demonstrated using proton spectra of solids obtained under fast
magic-angle spinning. | cond-mat_stat-mech |
Sluggish Kinetics in the Parking Lot Model: We investigate, both analytically and by computer simulation, the kinetics of
a microscopic model of hard rods adsorbing on a linear substrate. For a small,
but finite desorption rate, the system reaches the equilibrium state very
slowly, and the long-time kinetics display three successive regimes: an
algebraic one where the density varies as $1/t$, a logarithmic one where the
density varies as $1/ln(t)$, followed by a terminal exponential approach. A
mean-field approach fails to predict the relaxation rate associated with the
latter. We show that the correct answer can only be provided by using a
systematic description based on a gap-distribution approach. | cond-mat_stat-mech |
Bi-Critical Central Point Of J FN -J SN Ising Model Phase Diagram: When interfaces between ordered domains are ordered clusters, frustration
disappears. A phase with mixed ordered structures emerges but no length scale
can be associated to. We show that sum of densities of each structure plays the
role of order parameter. For, we consider a regular half full lattice with
repulsive interaction extended to second neighboring particles. Ordered
structures are p(2X2) when ratio between second and first neighboring
interaction energies R=J SN /J FN <0.5 and degenerate p(2X1)/p(1X2) for R>0.5.
The ground states coexist with another named p(4X2)/p(2X4) at central
bi-critical point: a state to cross when passing between non-frustrated ordered
phases. | cond-mat_stat-mech |
Thermal noise of a cryo-cooled silicon cantilever locally heated up to
its melting point: The Fluctuation-Dissipation Theorem (FDT) is a powerful tool to estimate the
thermal noise of physical systems in equilibrium. In general however, thermal
equilibrium is an approximation, or cannot be assumed at all. A more general
formulation of the FDT is then needed to describe the behavior of the
fluctuations. In our experiment we study a micro-cantilever brought
out-ofequilibrium by a strong heat flux generated by the absorption of the
light of a laser. While the base is kept at cryogenic temperatures, the tip is
heated up to the melting point, thus creating the highest temperature
difference the system can sustain. We independently estimate the temperature
profile of the cantilever and its mechanical fluctuations, as well as its
dissipation. We then demonstrate how the thermal fluctuations of all the
observed degrees of freedom, though increasing with the heat flux, are much
lower than what is expected from the average temperature of the system. We
interpret these results thanks to a minimal extension of the FDT: this dearth
of thermal noise arises from a dissipation shared between clamping losses and
distributed damping. | cond-mat_stat-mech |
Short-range Ising spin glasses: the metastate interpretation of replica
symmetry breaking: Parisi's formal replica-symmetry--breaking (RSB) scheme for mean-field spin
glasses has long been interpreted in terms of many pure states organized
ultrametrically. However, the early version of this interpretation, as applied
to the short-range Edwards-Anderson model, runs into problems because as shown
by Newman and Stein (NS) it does not allow for chaotic size dependence, and
predicts non-self-averaging that cannot occur. NS proposed the concept of the
metastate (a probability distribution over infinite-size Gibbs states in a
given sample that captures the effects of chaotic size dependence) and a
non-standard interpretation of the RSB results in which the metastate is
non-trivial and is responsible for what was called non-self-averaging. Here we
use the effective field theory of RSB, in conjunction with the rigorous
definitions of pure states and the metastate in infinite-size systems, to show
that the non-standard picture follows directly from the RSB mean-field theory.
In addition, the metastate-averaged state possesses power-law correlations
throughout the low temperature phase; the corresponding exponent $\zeta$ takes
the value $4$ according to the field theory in high dimensions $d$, and
describes the effective fractal dimension of clusters of spins. Further, the
logarithm of the number of pure states in the decomposition of the
metastate-averaged state that can be distinguished if only correlations in a
window of size $W$ can be observed is of order $W^{d-\zeta}$. These results
extend the non-standard picture quantitatively; we show that arguments against
this scenario are inconclusive. | cond-mat_stat-mech |
Tsallis nonextensive statistical mechanics of El Nino Southern
Oscillation Index: The shape and tails of partial distribution functions (PDF) for a
climatological signal, i.e. the El Nino SOI and the turbulent nature of the
ocean-atmosphere variability are linked through a model encompassing Tsallis
nonextensive statistics and leading to evolution equations of the Langevin and
Fokker-Planck type. A model originally proposed to describe the intermittent
behavior of turbulent flows describes the behavior of the normalized
variability for such a climatological index, for small and large time windows,
both for small and large variability. This normalized variabil- ity
distributions can be sufficiently well fitted with a chi-square-distribution.
The transition between the small time scale model of nonextensive, intermittent
process and the large scale Gaussian exten- sive homogeneous fluctuation
picture is found to occur at above ca. a 48 months time lag. The intermittency
exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is
found to be related to the scaling exponent of the PDF moments. The value of
$\kappa$ (= 0.25) is in agreement with the intermittency exponent recently
obtained for other atmospheric data. | cond-mat_stat-mech |
Exact solution for a sample space reducing stochastic process: Stochastic processes wherein the size of the state space is changing as a
function of time offer models for the emergence of scale-invariant features
observed in complex systems. I consider such a sample-space reducing (SSR)
stochastic process that results in a random sequence of strictly decreasing
integers $\{x(t)\}$, $0\le t \le \tau$, with boundary conditions $x(0) = N$ and
$x(\tau)$ = 1. This model is shown to be exactly solvable:
$\mathcal{P}_N(\tau)$, the probability that the process survives for time
$\tau$ is analytically evaluated. In the limit of large $N$, the asymptotic
form of this probability distribution is Gaussian, with mean and variance both
varying logarithmically with system size: $\langle \tau \rangle \sim \ln N$ and
$\sigma_{\tau}^{2} \sim \ln N$. Correspondence can be made between survival
time statistics in the SSR process and record statistics of i.i.d. random
variables. | cond-mat_stat-mech |
Scaling laws for single-file diffusion of adhesive particles: Single-file diffusion refers to the Brownian motion in narrow channels where
particles cannot pass each other. In such processes, the diffusion of a tagged
particle is typically normal at short times and becomes subdiffusive at long
times. For hard-sphere interparticle interaction, the time-dependent mean
squared displacement of a tracer is well understood. Here we develop a scaling
theory for adhesive particles. It provides a full description of the
time-dependent diffusive behavior with a scaling function that depends on an
effective strength of adhesive interaction. Particle clustering induced by the
adhesive interaction slows down the diffusion at short times, while it enhances
subdiffusion at long times. The enhancement effect can be quantified in
measurements irrespective of how tagged particles are injected into the system.
Combined effects of pore structure and particle adhesiveness should speed up
translocation of molecules through narrow pores. | cond-mat_stat-mech |
Sensitivity of solid phase stability to the interparticle potential
range: studies of a new Lennard-Jones like model: In a recent article, Wang et al (Phys. Chem. Chem. Phys., 22, 10624 (2020))
introduced a new class of interparticle potential for molecular simulations.
The potential is defined by a single range parameter, eliminating the need to
decide how to truncate truly long-range interactions like the Lennard-Jones
(LJ) potential. The authors explored the phase diagram for a particular value
of the range parameter for which their potential is similar in shape to the LJ
12-6 potential. We have reevaluated the solid phase behaviour of this model
using both Lattice Switch Monte Carlo and thermodynamic integration. In
addition to finding that the boundary between hexagonal close packed (hcp) and
face centred cubic (fcc) phases presented by Wang et al was calculated
incorrectly, we show that owing to its finite range, the new potential exhibits
several 'artifact' reentrant transitions between hcp and fcc phases. The
artifact phases, which do not occur in the full (untruncated) LJ system, are
also found for typically adopted forms of the truncated and shifted LJ
potential. However, whilst in the latter case one can systematically
investigate and correct for the effects of the finite range on the calculated
phase behaviour, this is not possible for the new potential because the choice
of range parameter affects the entire potential shape. Our results highlight
that potentials with finite range may fail to represent the crystalline phase
behaviour of systems with long-range dispersion interactions, even
qualitatively. | cond-mat_stat-mech |
Introduction to Markov Chain Monte Carlo Simulations and their
Statistical Analysis: This article is a tutorial on Markov chain Monte Carlo simulations and their
statistical analysis. The theoretical concepts are illustrated through many
numerical assignments from the author's book on the subject. Computer code (in
Fortran) is available for all subjects covered and can be downloaded from the
web. | cond-mat_stat-mech |
Quantum Films Adsorbed on Graphite: Third and Fourth Helium Layers: Using a path-integral Monte Carlo method for simulating superfluid quantum
films, we investigate helium layers adsorbed on a substrate consisting of
graphite plus two solid helium layers. Our results for the promotion densities
and the dependence of the superfluid density on coverage are in agreement with
experiment. We can also explain certain features of the measured heat capacity
as a function of temperature and coverage. | cond-mat_stat-mech |
Memory and irreversibility on two-dimensional overdamped Brownian
dynamics: We consider the effects of memory on the stationary behavior of a
two-dimensional Langevin dynamics in a confining potential. The system is
treated in an overdamped approximation and the degrees of freedom are under the
influence of distinct kinds of stochastic forces, described by Gaussian white
and colored noises, as well as different effective temperatures. The joint
distribution function is calculated by time-averaging approaches, and the
long-term behavior is analyzed. We determine the influence of noise temporal
correlations on the steady-state behavior of heat flux and entropy production.
Non-Markovian effects lead to a decaying heat exchange with spring force
parameter, which is in contrast to the usual linear dependence when only
Gaussian white noises are presented in overdamped treatments. Also, the model
exhibits non-equilibrium states characterized by a decreasing entropy
production with memory time-scale. | cond-mat_stat-mech |
Cascading Dynamics in Modular Networks: In this paper we study a simple cascading process in a structured
heterogeneous population, namely, a network composed of two loosely coupled
communities. We demonstrate that under certain conditions the cascading
dynamics in such a network has a two--tiered structure that characterizes
activity spreading at different rates in the communities. We study the dynamics
of the model using both simulations and an analytical approach based on
annealed approximation, and obtain good agreement between the two. Our results
suggest that network modularity might have implications in various
applications, such as epidemiology and viral marketing. | cond-mat_stat-mech |
Asymmetric temperature equilibration with heat flow from cold to hot in
a quantum thermodynamic system: A model computational quantum thermodynamic network is constructed with two
variable temperature baths coupled by a linker system, with an asymmetry in the
coupling of the linker to the two baths. It is found in computational
simulations that the baths come to "thermal equilibrium" at different bath
energies and temperatures. In a sense, heat is observed to flow from cold to
hot. A description is given in which a recently defined quantum entropy
$S^Q_{univ}$ for a pure state "universe" continues to increase after passing
through the classical equilibrium point of equal temperatures, reaching a
maximum at the asymmetric equilibrium. Thus, a second law account $\Delta
S^Q_{univ} \ge 0$ holds for the asymmetric quantum process. In contrast, a von
Neumann entropy description fails to uphold the entropy law, with a maximum
near when the two temperatures are equal, then a decrease $\Delta S^{vN} < 0$
on the way to the asymmetric equilibrium. | cond-mat_stat-mech |
Reaction Front in an A+B -> C Reaction-Subdiffusion Process: We study the reaction front for the process A+B -> C in which the reagents
move subdiffusively. Our theoretical description is based on a fractional
reaction-subdiffusion equation in which both the motion and the reaction terms
are affected by the subdiffusive character of the process. We design numerical
simulations to check our theoretical results, describing the simulations in
some detail because the rules necessarily differ in important respects from
those used in diffusive processes. Comparisons between theory and simulations
are on the whole favorable, with the most difficult quantities to capture being
those that involve very small numbers of particles. In particular, we analyze
the total number of product particles, the width of the depletion zone, the
production profile of product and its width, as well as the reactant
concentrations at the center of the reaction zone, all as a function of time.
We also analyze the shape of the product profile as a function of time, in
particular its unusual behavior at the center of the reaction zone. | cond-mat_stat-mech |
Constructing smooth potentials of mean force, radial, distribution
functions and probability densities from sampled data: In this paper a method of obtaining smooth analytical estimates of
probability densities, radial distribution functions and potentials of mean
force from sampled data in a statistically controlled fashion is presented. The
approach is general and can be applied to any density of a single random
variable. The method outlined here avoids the use of histograms, which require
the specification of a physical parameter (bin size) and tend to give noisy
results. The technique is an extension of the Berg-Harris method [B.A. Berg and
R.C. Harris, Comp. Phys. Comm. 179, 443 (2008)], which is typically inaccurate
for radial distribution functions and potentials of mean force due to a
non-uniform Jacobian factor. In addition, the standard method often requires a
large number of Fourier modes to represent radial distribution functions, which
tends to lead to oscillatory fits. It is shown that the issues of poor sampling
due to a Jacobian factor can be resolved using a biased resampling scheme,
while the requirement of a large number of Fourier modes is mitigated through
an automated piecewise construction approach. The method is demonstrated by
analyzing the radial distribution functions in an energy-discretized water
model. In addition, the fitting procedure is illustrated on three more
applications for which the original Berg-Harris method is not suitable, namely,
a random variable with a discontinuous probability density, a density with long
tails, and the distribution of the first arrival times of a diffusing particle
to a sphere, which has both long tails and short-time structure. In all cases,
the resampled, piecewise analytical fit outperforms the histogram and the
original Berg-Harris method. | cond-mat_stat-mech |
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