text
stringlengths 89
2.49k
| category
stringclasses 19
values |
|---|---|
Finite-size scaling of the random-field Ising model above the upper
critical dimension: Finite-size scaling above the upper critical dimension is a long-standing
puzzle in the field of Statistical Physics. Even for pure systems various
scaling theories have been suggested, partially corroborated by numerical
simulations. In the present manuscript we address this problem in the even more
complicated case of disordered systems. In particular, we investigate the
scaling behavior of the random-field Ising model at dimension $D = 7$, i.e.,
above its upper critical dimension $D_{\rm u} = 6$, by employing extensive
ground-state numerical simulations. Our results confirm the hypothesis that at
dimensions $D > D_{\rm u}$, linear length scale $L$ should be replaced in
finite-size scaling expressions by the effective scale $L_{\rm eff} = L^{D /
D_{\rm u}}$. Via a fitted version of the quotients method that takes this
modification, but also subleading scaling corrections into account, we compute
the critical point of the transition for Gaussian random fields and provide
estimates for the full set of critical exponents. Thus, our analysis indicates
that this modified version of finite-size scaling is successful also in the
context of the random-field problem. | cond-mat_stat-mech |
Phase Separation Transition in a Nonconserved Two Species Model: A one dimensional stochastic exclusion process with two species of particles,
$+$ and $-$, is studied where density of each species can fluctuate but the
total particle density is conserved. From the exact stationary state weights we
show that, in the limiting case where density of negative particles vanishes,
the system undergoes a phase separation transition where a macroscopic domain
of vacancies form in front of a single surviving negative particle. We also
show that the phase separated state is associated with a diverging correlation
length for any density and the critical exponents characterizing the behaviour
in this region are different from those at the transition line. The static and
the dynamical critical exponents are obtained from the exact solution and
numerical simulations, respectively. | cond-mat_stat-mech |
Duality between random trap and barrier models: We discuss the physical consequences of a duality between two models with
quenched disorder, in which particles propagate in one dimension among random
traps or across random barriers. We derive an exact relation between their
diffusion fronts at fixed disorder, and deduce from this that their
disorder-averaged diffusion fronts are exactly equal. We use effective dynamics
schemes to isolate the different physical processes by which particles
propagate in the models and discuss how the duality arises from a
correspondence between the rates for these different processes. | cond-mat_stat-mech |
Marginal and Conditional Second Laws of Thermodynamics: We consider the entropy production of a strongly coupled bipartite system.
The total entropy production can be partitioned into various components, which
we use to define local versions of the Second Law that are valid without the
usual idealization of weak coupling. The key insight is that causal
intervention offers a way to identify those parts of the entropy production
that result from feedback between the sub-systems. From this the central
relations describing the thermodynamics of strongly coupled systems follow in a
few lines. | cond-mat_stat-mech |
Screening of an electrically charged particle in a two-dimensional
two-component plasma at $Γ=2$: We consider the thermodynamic effects of an electrically charged impurity
immersed in a two-dimensional two-component plasma, composed by particles with
charges $\pm e$, at temperature $T$, at coupling $\Gamma=e^2/(k_B T)=2$,
confined in a large disk of radius $R$. Particularly, we focus on the analysis
of the charge density, the correlation functions, and the grand potential. Our
analytical results show how the charges are redistributed in the circular
geometry considered here. When we consider a positively charged impurity, the
negative ions accumulate close to the impurity leaving an excess of positive
charge that accumulates at the boundary of the disk. Due to the symmetry under
charge exchange, the opposite effect takes place when we place a negative
impurity. Both the cases in which the impurity charge is an integer multiple of
the particle charges in the plasma, $\pm e$, and a fraction of them are
considered; both situations require a slightly different mathematical
treatments, showing the effect of the quantization of plasma charges. The bulk
and tension effects in the plasma described by the grand potential are not
modified by the introduction of the charged particle. Besides the effects due
to the collapse coming from the attraction between oppositely charged ions, an
additional topological term appears in the grand potential, proportional to
$-n^2\ln(mR)$, with $n$ the dimensionless charge of the particle. This term
modifies the central charge of the system, from $c=1$ to $c=1-6n^2$, when
considered in the context of conformal field theories. | cond-mat_stat-mech |
Fractional differential and integral operations and cumulative processes: In this study the general formula for differential and integral operations of
fractional calculus via fractal operators by the method of cumulative
diminution and cumulative growth is obtained. The under lying mechanism in the
success of traditional fractional calculus for describing complex systems is
uncovered. The connection between complex physics with fractional
differentiation and integration operations is established. | cond-mat_stat-mech |
Trapping of an active Brownian particle at a partially absorbing wall: Active matter concerns the self-organization of energy consuming elements
such as motile bacteria or self-propelled colloids. A canonical example is an
active Brownian particle (ABP) that moves at constant speed while its direction
of motion undergoes rotational diffusion. When ABPs are confined within a
channel, they tend to accumulate at the channel walls, even when inter-particle
interactions are ignored. Each particle pushes on the boundary until a tumble
event reverses its direction. The wall thus acts as a sticky boundary. In this
paper we consider a natural extension of sticky boundaries that allows for a
particle to be permanently killed (absorbed) whilst attached to a wall. In
particular, we investigate the first passage time (FPT) problem for an ABP in a
two-dimensional channel where one of the walls is partially absorbing.
Calculating the exact FPT statistics requires solving a non-trivial two-way
diffusion boundary value problem (BVP). We follow a different approach by
separating out the dynamics away from the absorbing wall from the dynamics of
absorption and escape whilst attached to the wall. Using probabilistic methods,
we derive an explicit expression for the MFPT of absorption, assuming that the
arrival statistics of particles at the wall are known. Our method also allows
us to incorporate a more general encounter-based model of absorption. | cond-mat_stat-mech |
Dynamics of Eulerian walkers: We investigate the dynamics of Eulerian walkers as a model of self-organized
criticality. The evolution of the system is subdivided into characteristic
periods which can be seen as avalanches. The structure of avalanches is
described and the critical exponent in the distribution of first avalanches
$\tau=2$ is determined. We also study a mean square displacement of Eulerian
walkers and obtain a simple diffusion law in the critical state. The evolution
of underlying medium from a random state to the critical one is also described. | cond-mat_stat-mech |
Long-wavelength instabilities in a system of interacting active
particles: Based on a microscopic model, we develop a continuum description for a
suspension of microscopic self propelled particles. With this continuum
description we study the role of long-range interactions in destabilizing
macroscopic ordered phases that are developed by short-range interactions.
Long-wavelength fluctuations can destabilize both isotropic and also symmetry
broken polar phase in a suspension of dipolar particles. The instabilities in a
suspension of pullers (pushers) arise from splay (bend) fluctuations. Such
instabilities are not seen in a suspension of quadrupolar particles. | cond-mat_stat-mech |
Robustness of a perturbed topological phase: We investigate the stability of the topological phase of the toric code model
in the presence of a uniform magnetic field by means of variational and
high-order series expansion approaches. We find that when this perturbation is
strong enough, the system undergoes a topological phase transition whose first-
or second-order nature depends on the field orientation. When this transition
is of second order, it is in the Ising universality class except for a special
line on which the critical exponent driving the closure of the gap varies
continuously, unveiling a new topological universality class. | cond-mat_stat-mech |
Disorder Driven Roughening Transitions of Elastic Manifolds and Periodic
Elastic Media: The simultaneous effect of both disorder and crystal-lattice pinning on the
equilibrium behavior of oriented elastic objects is studied using scaling
arguments and a functional renormalization group technique. Our analysis
applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic
media, e.g., charge-density waves or flux-line lattices. The competition
between both pinning mechanisms leads to a continuous, disorder driven
roughening transition between a flat state where the mean relative displacement
saturates on large scales and a rough state with diverging relative
displacement. The transition can be approached by changing the impurity
concentration or, indirectly, by tuning the temperature since the pinning
strengths of the random and crystal potential have in general a different
temperature dependence. For D dimensional elastic manifolds interacting with
either random-field or random-bond disorder a transition exists for 2<D<4, and
the critical exponents are obtained to lowest order in \epsilon=4-D. At the
transition, the manifolds show a superuniversal logarithmic roughness. Dipolar
interactions render lattice effects relevant also in the physical case of D=2.
For periodic elastic media, a roughening transition exists only if the ratio p
of the periodicities of the medium and the crystal lattice exceeds the critical
value p_c=6/\pi\sqrt{\epsilon}. For p<p_c the medium is always flat. Critical
exponents are calculated in a double expansion in \mu=p^2/p_c^2-1 and
\epsilon=4-D and fulfill the scaling relations of random field models. | cond-mat_stat-mech |
The quantum (non-Abelian) Potts model and its exact solution: We generalize the classical one dimensional Potts model to the case where the
symmetry group is a non-Abelian finite group. It turns out that this new model
has a quantum nature in that its spectrum of energy eigenstates consists of
entangled states. We determine the complete energy spectrum, i.e. the ground
states and all the excited states with their degeneracy structure. We calculate
the partition function by two different algebraic and combinatorial methods. We
also determine the entanglement properties of its ground states. | cond-mat_stat-mech |
A memory-induced diffusive-superdiffusive transition: ensemble and
time-averaged observables: The ensemble properties and time-averaged observables of a memory-induced
diffusive-superdiffusive transition are studied. The model consists in a random
walker whose transitions in a given direction depend on a weighted linear
combination of the number of both right and left previous transitions. The
diffusion process is nonstationary and its probability develops the phenomenon
of aging. Depending on the characteristic memory parameters, the ensemble
behavior may be normal, superdiffusive, or ballistic. In contrast, the
time-averaged mean squared displacement is equal to that of a normal undriven
random walk, which renders the process non-ergodic. In addition, and similarly
to Levy walks [Godec and Metzler, Phys. Rev. Lett. 110, 020603 (2013)], for
trajectories of finite duration the time-averaged displacement apparently
become random with properties that depend on the measurement time and also on
the memory properties. These features are related to the non-stationary
power-law decay of the transition probabilities to their stationary values.
Time-averaged response to a bias is also calculated. In contrast with Levy
walks [Froemberg and Barkai, Phys. Rev. E 87, 030104(R) (2013)], the response
always vanishes asymptotically. | cond-mat_stat-mech |
Hierarchy Bloch Equations for the Reduced Statistical Density Operators
in Canonical and Grand canonical Ensembles: Starting from Bloch equation for a canonical ensemble, we deduce a set of
hierarchy equations for the reduced statistical density operator for an
identical many-body system with two-body interaction. They provide a law
according to which the reduced density operator varies in temperature. By
definition of the reduced density operator in Fock space for a grand canonical
ensemble, we also obtain the analogous Bloch equation and the corresponding
hierarchy reduced equations for the identical interacting many-body system. We
discuss their possible solutions and applications. | cond-mat_stat-mech |
String Method for Generalized Gradient Flows: Computation of Rare Events
in Reversible Stochastic Processes: Rare transitions in stochastic processes can often be rigorously described
via an underlying large deviation principle. Recent breakthroughs in the
classification of reversible stochastic processes as gradient flows have led to
a connection of large deviation principles to a generalized gradient structure.
Here, we show that, as a consequence, metastable transitions in these
reversible processes can be interpreted as heteroclinic orbits of the
generalized gradient flow. This in turn suggests a numerical algorithm to
compute the transition trajectories in configuration space efficiently, based
on the string method traditionally restricted only to gradient diffusions. | cond-mat_stat-mech |
Distribution of extremes in the fluctuations of two-dimensional
equilibrium interfaces: We investigate the statistics of the maximal fluctuation of two-dimensional
Gaussian interfaces. Its relation to the entropic repulsion between rigid walls
and a confined interface is used to derive the average maximal fluctuation $<m>
\sim \sqrt{2/(\pi K)} \ln N$ and the asymptotic behavior of the whole
distribution $P(m) \sim N^2 e^{-{\rm (const)} N^2 e^{-\sqrt{2\pi K} m} -
\sqrt{2\pi K} m}$ for $m$ finite with $N^2$ and $K$ the interface size and
tension, respectively. The standardized form of $P(m)$ does not depend on $N$
or $K$, but shows a good agreement with Gumbel's first asymptote distribution
with a particular non-integer parameter. The effects of the correlations among
individual fluctuations on the extreme value statistics are discussed in our
findings. | cond-mat_stat-mech |
Symmetry decomposition of negativity of massless free fermions: We consider the problem of symmetry decomposition of the entanglement
negativity in free fermionic systems. Rather than performing the standard
partial transpose, we use the partial time-reversal transformation which
naturally encodes the fermionic statistics. The negativity admits a resolution
in terms of the charge imbalance between the two subsystems. We introduce a
normalised version of the imbalance resolved negativity which has the advantage
to be an entanglement proxy for each symmetry sector, but may diverge in the
limit of pure states for some sectors. Our main focus is then the resolution of
the negativity for a free Dirac field at finite temperature and size. We
consider both bipartite and tripartite geometries and exploit conformal field
theory to derive universal results for the charge imbalance resolved
negativity. To this end, we use a geometrical construction in terms of an
Aharonov-Bohm-like flux inserted in the Riemann surface defining the
entanglement. We interestingly find that the entanglement negativity is always
equally distributed among the different imbalance sectors at leading order. Our
analytical findings are tested against exact numerical calculations for free
fermions on a lattice. | cond-mat_stat-mech |
Non-universal dynamics of dimer growing interfaces: A finite temperature version of body-centered solid-on-solid growth models
involving attachment and detachment of dimers is discussed in 1+1 dimensions.
The dynamic exponent of the growing interface is studied numerically via the
spectrum gap of the underlying evolution operator. The finite size scaling of
the latter is found to be affected by a standard surface tension term on which
the growth rates depend. This non-universal aspect is also corroborated by the
growth behavior observed in large scale simulations. By contrast, the
roughening exponent remains robust over wide temperature ranges. | cond-mat_stat-mech |
Non Commutative Geometry of Tilings and Gap Labelling: To a given tiling a non commutative space and the corresponding C*-algebra
are constructed. This includes the definition of a topology on the groupoid
induced by translations of the tiling. The algebra is also the algebra of
observables for discrete models of one or many particle systems on the tiling
or its periodic identification. Its scaled ordered K_0-group furnishes the gap
labelling of Schroedinger operators. The group is computed for one dimensional
tilings and Cartesian products thereof. Its image under a state is investigated
for tilings which are invariant under a substitution. Part of this image is
given by an invariant measure on the hull of the tiling which is determined.
The results from the Cartesian products of one dimensional tilings point out
that the gap labelling by means of the values of the integrated density of
states is already fully determined by this measure. | cond-mat_stat-mech |
Blind calibration for compressed sensing: State evolution and an online
algorithm: Compressed sensing, allows to acquire compressible signals with a small
number of measurements. In applications, a hardware implementation often
requires a calibration as the sensing process is not perfectly known. Blind
calibration, that is performing at the same time calibration and compressed
sensing is thus particularly appealing. A potential approach was suggested by
Sch\"ulke and collaborators in Sch\"ulke et al. 2013 and 2015, using
approximate message passing (AMP) for blind calibration (cal-AMP). Here, the
algorithm is extended from the already proposed offline case to the online
case, where the calibration is refined step by step as new measured samples are
received. Furthermore, we show that the performance of both the offline and the
online algorithms can be theoretically studied via the State Evolution (SE)
formalism. Through numerical simulations, the efficiency of cal-AMP and the
consistency of the theoretical predictions are confirmed. | cond-mat_stat-mech |
Ageing of complex networks: Many real-world complex networks arise as a result of a competition between
growth and rewiring processes. Usually the initial part of the evolution is
dominated by growth while the later one rather by rewiring. The initial growth
allows the network to reach a certain size while rewiring to optimise its
function and topology. As a model example we consider tree networks which first
grow in a stochastic process of node attachment and then age in a stochastic
process of local topology changes. The ageing is implemented as a Markov
process that preserves the node-degree distribution. We quantify differences
between the initial and aged network topologies and study the dynamics of the
evolution. We implement two versions of the ageing dynamics. One is based on
reshuffling of leaves and the other on reshuffling of branches. The latter one
generates much faster ageing due to non-local nature of changes. | cond-mat_stat-mech |
Anomalous scaling in statistical models of passively advected vector
fields: The field theoretic renormalization group and the operator product expansion
are applied to the stochastic model of passively advected vector field with the
most general form of the nonlinear term allowed by the Galilean symmetry. The
advecting turbulent velocity field is governed by the stochastic Navier--Stokes
equation. It is shown that the correlation functions of the passive vector
field in the inertial range exhibit anomalous scaling behaviour. The
corresponding anomalous exponents are determined by the critical dimensions of
tensor composite fields (operators) built solely of the passive vector field.
They are calculated (including the anisotropic sectors) in the leading order of
the expansion in $y$, the exponent entering the correlator of the stirring
force in the Navier--Stokes equation (one-loop approximation of the
renormalization group). The anomalous exponents exhibit an hierarchy related to
the degree of anisotropy: the less is the rank of the tensor operator, the less
is its dimension. Thus the leading terms, determined by scalar operators, are
the same as in the isotropic case, in agreement with the Kolmogorov's
hypothesis of the local isotropy restoration. | cond-mat_stat-mech |
Some geometric critical exponents for percolation and the random-cluster
model: We introduce several infinite families of new critical exponents for the
random-cluster model and present scaling arguments relating them to the k-arm
exponents. We then present Monte Carlo simulations confirming these
predictions. These new exponents provide a convenient way to determine k-arm
exponents from Monte Carlo simulations. An understanding of these exponents
also leads to a radically improved implementation of the Sweeny Monte Carlo
algorithm. In addition, our Monte Carlo data allow us to conjecture an exact
expression for the shortest-path fractal dimension d_min in two dimensions:
d_min = (g+2)(g+18)/(32g) where g is the Coulomb-gas coupling, related to the
cluster fugacity q via q = 2 + 2 cos(g\pi/2) with 2 \le g \le 4. | cond-mat_stat-mech |
Kinetic Ising model in an oscillating field: Avrami theory for the
hysteretic response and finite-size scaling for the dynamic phase transition: Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor,
kinetic Ising ferromagnet in an oscillating field, using Monte Carlo
simulations and analytical theory. Attention is focused on large systems and
strong field amplitudes at a temperature below T_c. In this parameter regime,
the magnetization switches through random nucleation and subsequent growth of
many droplets of spins aligned with the applied field. Using a time-dependent
extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable
decay, we analyze the statistical properties of the hysteresis-loop area and
the correlation between the magnetization and the applied field. This analysis
enables us to accurately predict the results of extensive Monte Carlo
simulations. The average loop area exhibits an extremely slow approach to an
asymptotic, logarithmic dependence on the product of the amplitude and the
frequency of the applied field. This may explain the inconsistent exponent
estimates reported in previous attempts to fit experimental and numerical data
for the low-frequency behavior of this quantity to a power law. At higher
frequencies we observe a dynamic phase transition. Applying standard
finite-size scaling techniques from the theory of second-order equilibrium
phase transitions to this nonequilibrium phase transition, we obtain estimates
for the transition frequency and the critical exponents (beta/nu \approx 0.11,
gamma/nu \approx 1.84 and nu \approx 1.1). In addition to their significance
for the interpretation of recent experiments on switching in ferromagnetic and
ferroelectric nanoparticles and thin films, our results provide evidence for
the relevance of universality and finite-size scaling to dynamic phase
transitions in spatially extended nonstationary systems. | cond-mat_stat-mech |
Finite temperature vortex dynamics in Bose Einstein condensates: We study the decay of vortices in Bose-Einstein condensates at finite
temperatures by means of the Zaremba Nikuni Griffin formalism, in which the
condensate is modelled by a Gross Pitaevskiiequation, which is coupled to a
Boltzmann kinetic equation for the thermal cloud. At finite temperature, an
off-centred vortex in a harmonically trapped pancake shaped condensate decays
by spiralling out towards the edge of the condensate. This decay, which depends
heavily on temperature and atomic collisions, agrees with that predicted by the
Hall Vinen phenomenological model of friction force, which is used to describe
quantised vorticity in superfluid systems. Our result thus clarifies the
microscopic origin of the friction and provides an ab initio determination of
its value. | cond-mat_stat-mech |
On the transport of interacting particles in a chain of cavities:
Description through a modified Fick-Jacobs equation: We study the transport process of interacting Brownian particles in a tube of
varying cross section. To describe this process we introduce a modified
Fick-Jacobs equation, considering particles that interact through a hard-core
potential. We were able to solve the equation with numerical methods for the
case of symmetric and asymmetric cavities. We focused in the concentration of
particles along the direction of the tube. We also preformed Monte Carlo
simulations to evaluate the accuracy of the results, obtaining good agreement
between theory and simulations. | cond-mat_stat-mech |
Low-rank Monte Carlo for Smoluchowski-class equations: The work discusses a new low-rank Monte Carlo technique to solve
Smoluchowski-like kinetic equations. It drastically decreases the computational
complexity of modeling of size-polydisperse systems. For the studied systems it
can outperform the existing methods by more than ten times; its superiority
further grows with increasing system size. Application to the recently
developed temperature-dependent Smoluchowski equations is also demonstrated. | cond-mat_stat-mech |
Kinetic roughening model with opposite Kardar-Parisi-Zhang
nonlinearities: We introduce a model that simulates a kinetic roughening process with two
kinds of particles: one follows the ballistic deposition (BD) kinetic and, the
other, the restricted solid-on-solid (KK) kinetic. Both of these kinetics are
in the universality class of the nonlinear KPZ equation, but the BD kinetic has
a positive nonlinear constant while the KK kinetic has a negative one. In our
model, called BD-KK model, we assign the probabilities p and (1-p) to the KK
and BD kinetics, respectively. For a specific value of p, the system behaves as
a quasi linear model and the up-down symmetry is recuperated. We show that
nonlinearities of odd-order are relevant in these low nonlinear limit. | cond-mat_stat-mech |
Critical behavior of the planar magnet model in three dimensions: We use a hybrid Monte Carlo algorithm in which a single-cluster update is
combined with the over-relaxation and Metropolis spin re-orientation algorithm.
Periodic boundary conditions were applied in all directions. We have calculated
the fourth-order cumulant in finite size lattices using the single-histogram
re-weighting method. Using finite-size scaling theory, we obtained the critical
temperature which is very different from that of the usual XY model. At the
critical temperature, we calculated the susceptibility and the magnetization on
lattices of size up to $42^3$. Using finite-size scaling theory we accurately
determine the critical exponents of the model and find that $\nu$=0.670(7),
$\gamma/\nu$=1.9696(37), and $\beta/\nu$=0.515(2). Thus, we conclude that the
model belongs to the same universality class with the XY model, as expected. | 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 |
Spatial Particle Condensation for an Exclusion Process on a Ring: We study the stationary state of a simple exclusion process on a ring which
was recently introduced by Arndt {\it et al} [J. Phys. A {\bf 31} (1998)
L45;cond-mat/9809123]. This model exhibits spatial condensation of particles.
It has been argued that the model has a phase transition from a ``mixed phase''
to a ``disordered phase''. However, in this paper exact calculations are
presented which, we believe, show that in the framework of a grand canonical
ensemble there is no such phase transition. An analysis of the fluctuations in
the particle density strongly suggests that the same result also holds for the
canonical ensemble. | cond-mat_stat-mech |
Random matrices applications to soft spectra: It recently has been found that methods of the statistical theories of
spectra can be a useful tool in the analysis of spectra far from levels of
Hamiltonian systems. Several examples originate from areas, such as
quantitative linguistics and polymers. The purpose of the present study is to
deepen this kind of approach by performing a more comprehensive spectral
analysis that measures both the local and long-range statistics. We have found
that, as a common feature, spectra of this kind can exhibit a situation in
which local statistics are relatively quenched while the long range ones show
large fluctuations. By combining extensions of the standard Random Matrix
Theory (RMT) and considering long spectra, we demonstrate that this phenomenon
occurs when weak disorder is introduced in a RMT spectrum or when strong
disorder acts in a Poisson regime. We show that the long-range statistics
follow the Taylor law, which suggests the presence of a fluctuation scaling
(FS) mechanism in this kind of spectra. | cond-mat_stat-mech |
Reaction Diffusion and Ballistic Annihilation Near an Impenetrable
Boundary: The behavior of the single-species reaction process $A+A\to O$ is examined
near an impenetrable boundary, representing the flask containing the reactants.
Two types of dynamics are considered for the reactants: diffusive and ballistic
propagation. It is shown that the effect of the boundary is quite different in
both cases: diffusion-reaction leads to a density excess, whereas ballistic
annihilation exhibits a density deficit, and in both cases the effect is not
localized at the boundary but penetrates into the system. The field-theoretic
renormalization group is used to obtain the universal properties of the density
excess in two dimensions and below for the reaction-diffusion system. In one
dimension the excess decays with the same exponent as the bulk and is found by
an exact solution. In two dimensions the excess is marginally less relevant
than the bulk decay and the density profile is again found exactly for late
times from the RG-improved field theory. The results obtained for the diffusive
case are relevant for Mg$^{2+}$ or Cd$^{2+}$ doping in the TMMC crystal's
exciton coalescence process and also imply a surprising result for the dynamic
magnetization in the critical one-dimensional Ising model with a fixed spin.
For the case of ballistic reactants, a model is introduced and solved exactly
in one dimension. The density-deficit profile is obtained, as is the density of
left and right moving reactants near the impenetrable boundary. | cond-mat_stat-mech |
Kinetics of Ring Formation: We study reversible polymerization of rings. In this stochastic process, two
monomers bond and as a consequence, two disjoint rings may merge into a
compound ring, or, a single ring may split into two fragment rings. This
aggregation-fragmentation process exhibits a percolation transition with a
finite-ring phase in which all rings have microscopic length and a giant-ring
phase where macroscopic rings account for a finite fraction of the entire mass.
Interestingly, while the total mass of the giant rings is a deterministic
quantity, their total number and their sizes are stochastic quantities. The
size distribution of the macroscopic rings is universal, although the span of
this distribution increases with time. Moreover, the average number of giant
rings scales logarithmically with system size. We introduce a card-shuffling
algorithm for efficient simulation of the ring formation process, and present
numerical verification of the theoretical predictions. | cond-mat_stat-mech |
A Multicanonical Molecular Dynamics Study on a Simple Bead-Spring Model
for Protein Folding: We have performed a multicanonical molecular dynamics simulation on a simple
model protein.We have studied a model protein composed of charged, hydrophobic,
and neutral spherical bead monomers.Since the hydrophobic interaction is
considered to significantly affect protein folding, we particularly focus on
the competition between effects of the Coulomb interaction and the hydrophobic
interaction. We found that the transition which occurs upon decreasing the
temperature is markedly affected by the change in both parameters and forms of
the hydrophobic potential function, and the transition changes from first order
to second order, when the Coulomb interaction becomes weaker. | cond-mat_stat-mech |
Simulating first-order phase transition with hierarchical autoregressive
networks: We apply the Hierarchical Autoregressive Neural (HAN) network sampling
algorithm to the two-dimensional $Q$-state Potts model and perform simulations
around the phase transition at $Q=12$. We quantify the performance of the
approach in the vicinity of the first-order phase transition and compare it
with that of the Wolff cluster algorithm. We find a significant improvement as
far as the statistical uncertainty is concerned at a similar numerical effort.
In order to efficiently train large neural networks we introduce the technique
of pre-training. It allows to train some neural networks using smaller system
sizes and then employing them as starting configurations for larger system
sizes. This is possible due to the recursive construction of our hierarchical
approach. Our results serve as a demonstration of the performance of the
hierarchical approach for systems exhibiting bimodal distributions.
Additionally, we provide estimates of the free energy and entropy in the
vicinity of the phase transition with statistical uncertainties of the order of
$10^{-7}$ for the former and $10^{-3}$ for the latter based on a statistics of
$10^6$ configurations. | cond-mat_stat-mech |
Quantum fluctuation theorem for initial near-equilibrium system: Quantum work fluctuation theorem (FT) commonly requires the system initially
prepared in an equilibrium state. Whether there exists universal exact quantum
work FT for initial state beyond equilibrium needs further discussions. Here, I
initialize the system in a near-equilibrium state, and derive the corresponding
modified Jarzynski equality by using the perturbation theory. The correction is
nontrivial because it directly leads to the principle of maximum work or the
second law of thermodynamics for near-equilibrium system and also gives a much
tighter bound of work for a given process. I also verify my theoretical results
by considering a concrete many-body system, and reveal a fundamental connection
between quantum critical phenomenon and near-equilibrium state at really high
temperature. | cond-mat_stat-mech |
Kinetics of phase ordering on curved surfaces: An interface description and numerical simulations of model A kinetics are
used for the first time to investigate the intra-surface kinetics of phase
ordering on corrugated surfaces. Geometrical dynamical equations are derived
for the domain interfaces. The dynamics is shown to depend strongly on the
local Gaussian curvature of the surface, and can be fundamentally different
from that in flat systems: dynamical scaling breaks down despite the
persistence of the dominant interfacial undulation mode; growth laws are slower
than $t^{1/2}$ and even logarithmic; a new very-late-stage regime appears
characterized by extremely slow interface motion; finally, the zero-temperature
fixed point no longer exists, leading to metastable states. Criteria for the
existence of the latter are derived and discussed in the context of more
complex systems. | cond-mat_stat-mech |
The role of mobility in epidemics near criticality: The general epidemic process (GEP), also known as
susceptible-infected-recovered model (SIR), describes how an epidemic spreads
within a population of susceptible individuals who acquire permanent
immunization upon recovery. This model exhibits a second-order absorbing state
phase transition, commonly studied assuming immobile healthy individuals. We
investigate the impact of mobility on disease spreading near the extinction
threshold by introducing two generalizations of GEP, where the mobility of
susceptible and recovered individuals is examined independently. In both cases,
including mobility violates GEP's rapidity reversal symmetry and alters the
number of absorbing states. The critical dynamics of the models are analyzed
through a perturbative renormalization group approach and large-scale
stochastic simulations using a Gillespie algorithm. The renormalization group
analysis predicts both models to belong to the same novel universality class
describing the critical dynamics of epidemic spreading when the infected
individuals interact with a diffusive species and gain immunization upon
recovery. At the associated renormalization group fixed point, the immobile
species decouples from the dynamics of the infected species, dominated by the
coupling with the diffusive species. Numerical simulations in two dimensions
affirm our renormalization group results by identifying the same set of
critical exponents for both models. Violation of the rapidity reversal symmetry
is confirmed by breaking the associated hyperscaling relation. Our study
underscores the significance of mobility in shaping population spreading
dynamics near the extinction threshold. | cond-mat_stat-mech |
Vibrations of closed-shell Lennard-Jones icosahedral and cuboctahedral
clusters and their effect on the cluster ground state energy: Vibrational spectra of closed shell Lennard-Jones icosahedral and
cuboctahedral clusters are calculated for shell numbers between 2 and 9.
Evolution of the vibrational density of states with the cluster shell number is
examined and differences between icosahedral and cuboctahedral clusters
described. This enabled a quantum calculation of quantum ground state energies
of the clusters in the quasiharmonic approximation and a comparison of the
differences between the two types of clusters. It is demonstrated that in the
quantum treatment, the closed shell icosahedral clusters binding energies
differ from those of cuboctahedral clusters more than is the case in classical
treatment. | cond-mat_stat-mech |
Exclusion Processes and boundary conditions: A family of boundary conditions corresponding to exclusion processes is
introduced. This family is a generalization of the boundary conditions
corresponding to the simple exclusion process, the drop-push model, and the
one-parameter solvable family of pushing processes with certain rates on the
continuum [1-3]. The conditional probabilities are calculated using the Bethe
ansatz, and it is shown that at large times they behave like the corresponding
conditional probabilities of the family of diffusion-pushing processes
introduced in [1-3]. | cond-mat_stat-mech |
Extended Gibbs ensembles with flow: A statistical treatment of finite unbound systems in the presence of
collective motions is presented and applied to a classical Lennard-Jones
Hamiltonian, numerically simulated through molecular dynamics. In the ideal gas
limit, the flow dynamics can be exactly re-casted into effective time-dependent
Lagrange parameters acting on a standard Gibbs ensemble with an extra total
energy conservation constraint. Using this same ansatz for the low density
freeze-out configurations of an interacting expanding system, we show that the
presence of flow can have a sizeable effect on the microstate distribution. | cond-mat_stat-mech |
Microcanonical Monte Carlo Study of One Dimensional Self-Gravitating
Lattice Gas Models: In this study we present a Microcanonical Monte Carlo investigation of one
dimensional self-gravitating toy models. We study the effect of hard-core
potentials and compare to those results obtained with softening parameters and
also the effect of the geometry of the models. In order to study the effect of
the geometry and the borders in the system we introduce a model with the
symmetry of motion in a line instead of a circle, which we denominate as $1/r$
model. The hard-core particle potential introduces the effect of the size of
particles and, consequently, the effect of the density of the system that is
redefined in terms of the packing fraction of the system. The latter plays a
role similar to the softening parameter $\epsilon$ in the softened particles'
case. In the case of low packing fractions both models with hard-core particles
show a behavior that keeps the intrinsic properties of the three dimensional
gravitational systems such as negative heat capacity. For higher values of the
packing fraction the ring the system behaves as the Hamiltonian Mean Field
model and while for the $1/r$ it is similar to the one-dimensional systems. | cond-mat_stat-mech |
Empirical Traffic Data and Their Implications for Traffic Modeling: From single vehicle data a number of new empirical results about the temporal
evolution, correlation, and density-dependence of macroscopic traffic
quantities have been determined. These have relevant implications for traffic
modeling and allow to test existing traffic models. | cond-mat_stat-mech |
Two-dimensional scaling properties of experimental fracture surfaces: The morphology of fracture surfaces encodes the various complex damage and
fracture processes occurring at the microstructure scale that have lead to the
failure of a given heterogeneous material. Understanding how to decipher this
morphology is therefore of fundamental interest. This has been extensively
investigated over these two last decades. It has been established that 1D
profiles of these fracture surfaces exhibit properties of scaling invariance.
In this paper, we present deeper analysis and investigate the 2D scaling
properties of these fracture surfaces. We showed that the properties of scaling
invariance are anisotropic and evidenced the existence of two peculiar
directions on the post-mortem fracture surface caracterized by two different
scaling exponents: the direction of the crack growth and the direction of the
crack front. These two exponents were found to be universal, independent of the
crack growth velocity, in both silica glass and aluminum alloy, archetype of
brittle and ductile material respectively. Moreover, the 2D structure function
that fully characterizes the scaling properties of the fracture surface was
shown to take a peculiar form similar to the one predicted by some models
issued from out-of-equilibrium statistical physics. This suggest some promising
analogies between dynamic phase transition models and the stability of a crack
front pinned/unpinned by the heterogenities of the material. | cond-mat_stat-mech |
Correlated Percolation: Cluster concepts have been extremely useful in elucidating many problems in
physics. Percolation theory provides a generic framework to study the behavior
of the cluster distribution. In most cases the theory predicts a geometrical
transition at the percolation threshold, characterized in the percolative phase
by the presence of a spanning cluster, which becomes infinite in the
thermodynamic limit. Standard percolation usually deals with the problem when
the constitutive elements of the clusters are randomly distributed. However
correlations cannot always be neglected. In this case correlated percolation is
the appropriate theory to study such systems. The origin of correlated
percolation could be dated back to 1937 when Mayer [1] proposed a theory to
describe the condensation from a gas to a liquid in terms of mathematical
clusters (for a review of cluster theory in simple fluids see [2]). The
location for the divergence of the size of these clusters was interpreted as
the condensation transition from a gas to a liquid. One of the major drawback
of the theory was that the cluster number for some values of thermodynamic
parameters could become negative. As a consequence the clusters did not have
any physical interpretation [3]. This theory was followed by Frenkel's
phenomenological model [4], in which the fluid was considered as made of non
interacting physical clusters with a given free energy. This model was later
improved by Fisher [3], who proposed a different free energy for the clusters,
now called droplets, and consequently a different scaling form for the droplet
size distribution. This distribution, which depends on two geometrical
parameters, has the nice feature that the mean droplet size exhibits a
divergence at the liquid-gas critical point. | cond-mat_stat-mech |
Strong Correlations and Fickian Water Diffusion in Narrow Carbon
Nanotubes: We have used atomistic molecular dynamics (MD) simulations to study the
structure and dynamics of water molecules inside an open ended carbon nanotube
placed in a bath of water molecules. The size of the nanotube allows only a
single file of water molecules inside the nanotube. The water molecules inside
the nanotube show solid-like ordering at room temperature, which we quantify by
calculating the pair correlation function. It is shown that even for the
longest observation times, the mode of diffusion of the water molecules inside
the nanotube is Fickian and not sub-diffusive. We also propose a
one-dimensional random walk model for the diffusion of the water molecules
inside the nanotube. We find good agreement between the mean-square
displacements calculated from the random walk model and from MD simulations,
thereby confirming that the water molecules undergo normal-mode diffusion
inside the nanotube. We attribute this behavior to strong positional
correlations that cause all the water molecules inside the nanotube to move
collectively as a single object. The average residence time of the water
molecules inside the nanotube is shown to scale quadratically with the nanotube
length. | cond-mat_stat-mech |
Short range order in a steady state of irradiated Cu-Pd alloys:
Comparison with fluctuations at thermal equilibrium: The equilibrium short-range order (SRO) in Cu-Pd alloys is studied
theoretically. The evolution of the Fermi surface-related splitting of the
(110) diffuse intensity peak with changing temperature is examined. The results
are compared with experimental observations for electron-irradiated samples in
a steady state, for which the temperature dependence of the splitting was
previously found in the composition range from 20 to 28 at.% Pd. The
equilibrium state is studied by analysing available experimental and
theoretical results and using a recently proposed alpha-expansion theory of SRO
which is able to describe the temperature-dependent splitting. It is found that
the electronic-structure calculations in the framework of the
Korringa-Kohn-Rostoker coherent potential approximation overestimate the
experimental peak splitting. This discrepancy is attributed to the shift of the
intensity peaks with respect to the positions of the corresponding
reciprocal-space minima of the effective interatomic interaction towards the
(110) and equivalent positions. Combined with an assumption about monotonicity
of the temperature behaviour of the splitting, such shift implies an increase
of the splitting with increasing temperature for all compositions considered in
this study. The alpha-expansion calculations seem to confirm this conclusion. | cond-mat_stat-mech |
Conservation-laws-preserving algorithms for spin dynamics simulations: We propose new algorithms for numerical integration of the equations of
motion for classical spin systems with fixed spatial site positions. The
algorithms are derived on the basis of a mid-point scheme in conjunction with
the multiple time staging propagation. Contrary to existing predictor-corrector
and decomposition approaches, the algorithms introduced preserve all the
integrals of motion inherent in the basic equations. As is demonstrated for a
lattice ferromagnet model, the present approach appears to be more efficient
even over the recently developed decomposition method. | cond-mat_stat-mech |
On the statistical arrow of time: What is the physical origin of the arrow of time? It is a commonly held
belief in the physics community that it relates to the increase of entropy as
it appears in the statistical interpretation of the second law of
thermodynamics. At the same time, the subjective information-theoretical
interpretation of probability, and hence entropy, is a standard viewpoint in
the foundations of statistical mechanics. In this article, it is argued that
the subjective interpretation is incompatible with the philosophical point of
view that the arrow of time is a fundamental property of Nature. The
subjectivist can only uphold this philosophy if the role played by the second
law of thermodynamics in defining time's arrow is abandoned. | cond-mat_stat-mech |
Strongly-Coupled Coulomb Systems using finite-$T$ Density Functional
Theory: A review of studies on Strongly-Coupled Coulomb Systems since the
rise of DFT and SCCS-1977: The conferences on "Strongly Coupled Coulomb Systems" (SCCS) arose from the
"Strongly Coupled Plasmas" meetings, inaugurated in 1977. The progress in SCCS
theory is reviewed in an `author-centered' frame to limit its scope. Our
efforts, i.e., with Fran\c{c}ois Perrot, sought to apply density functional
theory (DFT) to SCCS calculations. DFT was then poised to become the major
computational scheme for condensed matter physics. The ion-sphere models of
Salpeter and others evolved into useful average-atom models for finite-$T$
Coulomb systems, as in Lieberman's Inferno code. We replaced these by
correlation-sphere models that exploit the description of matter via density
functionals linked to pair-distributions. These methods provided practical
computational means for studying strongly interacting electron-ion Coulomb
systems like warm-dense matter (WDM). The staples of SCCS are wide-ranged,
viz., equation of state, plasma spectroscopy, opacity (absorption, emission),
scattering, level shifts, transport properties, e.g., electrical and heat
conductivity, laser- and shock- created plasmas, their energy relaxation and
transient properties etc. These calculations need pseudopotentials and
exchange-correlation functionals applicable to finite-$T$ Coulomb systems that
may be used in ab initio codes, molecular dynamics, etc. The search for simpler
computational schemes has proceeded via proposals for orbital-free DFT,
statistical potentials, classical maps of quantum systems using classical
schemes like HNC to include strong coupling effects (CHNC). Laughlin's
classical plasma map for the fractional quantum Hall effect (FQHE) is a seminal
example where we report new results for graphene. | cond-mat_stat-mech |
Simple analytical model of a thermal diode: Recently there is a lot of attention given to manipulation of heat by
constructing thermal devices such as thermal diodes, transistors and logic
gates. Many of the models proposed have an asymmetry which leads to the desired
effect. Presence of non-linear interactions among the particles is also
essential. But, such models lack analytical understanding. Here we propose a
simple, analytically solvable model of a thermal diode. Our model consists of
classical spins in contact with multiple heat baths and constant external
magnetic fields. Interestingly the magnetic field is the only parameter
required to get the effect of heat rectification. | cond-mat_stat-mech |
Nonequilibrium coupled Brownian phase oscillators: A model of globally coupled phase oscillators under equilibrium (driven by
Gaussian white noise) and nonequilibrium (driven by symmetric dichotomic
fluctuations) is studied. For the equilibrium system, the mean-field state
equation takes a simple form and the stability of its solution is examined in
the full space of order parameters. For the nonequilbrium system, various
asymptotic regimes are obtained in a closed analytical form. In a general case,
the corresponding master equations are solved numerically. Moreover, the
Monte-Carlo simulations of the coupled set of Langevin equations of motion is
performed. The phase diagram of the nonequilibrium system is presented. For the
long time limit, we have found four regimes. Three of them can be obtained from
the mean-field theory. One of them, the oscillating regime, cannot be predicted
by the mean-field method and has been detected in the Monte-Carlo numerical
experiments. | cond-mat_stat-mech |
Granular fluid thermostatted by a bath of elastic hard spheres: The homogeneous steady state of a fluid of inelastic hard spheres immersed in
a bath of elastic hard spheres kept at equilibrium is analyzed by means of the
first Sonine approximation to the (spatially homogeneous) Enskog--Boltzmann
equation. The temperature of the granular fluid relative to the bath
temperature and the kurtosis of the granular distribution function are obtained
as functions of the coefficient of restitution, the mass ratio, and a
dimensionless parameter $\beta$ measuring the cooling rate relative to the
friction constant. Comparison with recent results obtained from an iterative
numerical solution of the Enskog--Boltzmann equation [Biben et al., Physica A
310, 308 (202)] shows an excellent agreement. Several limiting cases are also
considered. In particular, when the granular particles are much heavier than
the bath particles (but have a comparable size and number density), it is shown
that the bath acts as a white noise external driving. In the general case, the
Sonine approximation predicts the lack of a steady state if the control
parameter $\beta$ is larger than a certain critical value $\beta_c$ that
depends on the coefficient of restitution and the mass ratio. However, this
phenomenon appears outside the expected domain of applicability of the
approximation. | cond-mat_stat-mech |
Floquet dynamical quantum phase transitions under synchronized periodic
driving: We study a generic class of fermionic two-band models under synchronized
periodic driving, i.e., with the different terms in a Hamiltonian subject to
periodic drives with the same frequency and phase. With all modes initially in
a maximally mixed state, the synchronized drive is found to produce nonperiodic
patterns of dynamical quantum phase transitions, with their appearance
determined by an interplay of the band structure and the frequency of the
drive. A case study of the anisotropic XY chain in a transverse magnetic field,
transcribed to an effective two-band model, shows that the modes come with
quantized geometric phases, allowing for the construction of an effective
dynamical order parameter. Numerical studies in the limit of a strong magnetic
field reveal distinct signals of precursors of dynamical quantum phase
transitions also when the initial state of the XY chain is perturbed slightly
away from maximal mixing, suggesting that the transitions may be accessible
experimentally. A blueprint for an experiment built around laser-trapped
circular Rydberg atoms is proposed. | cond-mat_stat-mech |
Clusters in an epidemic model with long-range dispersal: In presence of long range dispersal, epidemics spread in spatially
disconnected regions known as clusters. Here, we characterize exactly their
statistical properties in a solvable model, in both the supercritical
(outbreak) and critical regimes. We identify two diverging length scales,
corresponding to the bulk and the outskirt of the epidemic. We reveal a
nontrivial critical exponent that governs the cluster number, the distribution
of their sizes and of the distances between them. We also discuss applications
to depinning avalanches with long range elasticity. | cond-mat_stat-mech |
Interplay among helical order, surface effects and range of interacting
layers in ultrathin films: The properties of helical thin films have been thoroughly investigated by
classical Monte Carlo simulations. The employed model assumes classical planar
spins in a body-centered tetragonal lattice, where the helical arrangement
along the film growth direction has been modeled by nearest neighbor and
next-nearest neighbor competing interactions, the minimal requirement to get
helical order. We obtain that, while the in-plane transition temperatures
remain essentially unchanged with respect to the bulk ones, the helical/fan
arrangement is stabilized at more and more low temperature when the film
thickness, n, decreases; in the ordered phase, increasing the temperature, a
softening of the helix pitch wave-vector is also observed. Moreover, we show
also that the simulation data around both transition temperatures lead us to
exclude the presence of a first order transition for all analyzed sizes.
Finally, by comparing the results of the present work with those obtained for
other models previously adopted in literature, we can get a deeper insight
about the entwined role played by the number (range) of interlayer interactions
and surface effects in non-collinear thin films. | cond-mat_stat-mech |
Extreme boundary conditions and random tilings: Standard statistical mechanical or condensed matter arguments tell us that
bulk properties of a physical system do not depend too much on boundary
conditions. Random tilings of large regions provide counterexamples to such
intuition, as illustrated by the famous 'arctic circle theorem' for dimer
coverings in two dimensions. In these notes, I discuss such examples in the
context of critical phenomena, and their relation to 1+1d quantum particle
models. All those turn out to share a common feature: they are inhomogeneous,
in the sense that local densities now depend on position in the bulk. I explain
how such problems may be understood using variational (or hydrodynamic)
arguments, how to treat long range correlations, and how non trivial edge
behavior can occur. While all this is done on the example of the dimer model,
the results presented here have much greater generality. In that sense the
dimer model serves as an opportunity to discuss broader methods and results.
[These notes require only a basic knowledge of statistical mechanics.] | cond-mat_stat-mech |
Universality of striped morphologies: We present a method for predicting the low-temperature behavior of spherical
and Ising spin models with isotropic potentials. For the spherical model the
characteristic length scales of the ground states are exactly determined but
the morphology is shown to be degenerate with checkerboard patterns, stripes
and more complex morphologies having identical energy. For the Ising models we
show that the discretization breaks the degeneracy causing striped morphologies
to be energetically favored and therefore they arise universally as ground
states to potentials whose Hankel transforms have nontrivial minima. | cond-mat_stat-mech |
Universal entanglement entropy in 2D conformal quantum critical points: We study the scaling behavior of the entanglement entropy of two dimensional
conformal quantum critical systems, i.e. systems with scale invariant wave
functions. They include two-dimensional generalized quantum dimer models on
bipartite lattices and quantum loop models, as well as the quantum Lifshitz
model and related gauge theories. We show that, under quite general conditions,
the entanglement entropy of a large and simply connected sub-system of an
infinite system with a smooth boundary has a universal finite contribution, as
well as scale-invariant terms for special geometries. The universal finite
contribution to the entanglement entropy is computable in terms of the
properties of the conformal structure of the wave function of these quantum
critical systems. The calculation of the universal term reduces to a problem in
boundary conformal field theory. | cond-mat_stat-mech |
Collective oscillations in driven coagulation: We present a novel form of collective oscillatory behavior in the kinetics of
irreversible coagulation with a constant input of monomers and removal of large
clusters. For a broad class of collision rates, this system reaches a
non-equilibrium stationary state at large times and the cluster size
distribution tends to a universal form characterised by a constant flux of mass
through the space of cluster sizes. Universality, in this context, means that
the stationary state becomes independent of the cut-off as the cut-off grows.
This universality is lost, however, if the aggregation rate between large and
small clusters increases sufficiently steeply as a function of cluster sizes.
We identify a transition to a regime in which the stationary state vanishes as
the cut-off grows. This non-universal stationary state becomes unstable,
however, as the cut-off is increased and undergoes a Hopf bifurcation. After
this bifurcation, the stationary kinetics are replaced by persistent and
periodic collective oscillations. These oscillations carry pulses of mass
through the space of cluster sizes. As a result, the average mass flux remains
constant. Furthermore, universality is partially restored in the sense that the
scaling of the period and amplitude of oscillation is inherited from the
dynamical scaling exponents of the universal regime. The implications of this
new type of long-time asymptotic behaviour for other driven non-equilibrium
systems are discussed. | cond-mat_stat-mech |
Extrapolating the thermodynamic length with finite-time measurements: The excess work performed in a heat-engine process with given finite
operation time \tau is bounded by the thermodynamic length, which measures the
distance during the relaxation along a path in the space of the thermodynamic
state. Unfortunately, the thermodynamic length, as a guidance for the heat
engine optimization, is beyond the experimental measurement. We propose to
measure the thermodynamic length \mathcal{L} through the extrapolation of
finite-time measurements
\mathcal{L}(\tau)=\int_{0}^{\tau}[P_{\mathrm{ex}}(t)]^{1/2}dt via the excess
power P_{\mathrm{ex}}(t). The current proposal allows to measure the
thermodynamic length for a single control parameter without requiring extra
effort to find the optimal control scheme. We illustrate the measurement
strategy via examples of the quantum harmonic oscillator with tuning frequency
and the classical ideal gas with changing volume. | cond-mat_stat-mech |
Monomer-Dimer Mixture on a Honeycomb Lattice: We study a monomer-dimer mixture defined on a honeycomb lattice as a toy
model for the spin ice system in a magnetic field. In a low-doping region of
monomers, the effective description of this system is given by the dual
sine-Gordon model. In intermediate- and strong-doping regions, the Potts
lattice gas theory can be employed. Synthesizing these results, we construct a
renormalization-group flow diagram, which includes the stable and unstable
fixed points corresponding to ${\cal M}_5$ and ${\cal M}_6$ in the minimal
models of the conformal field theory. We perform numerical transfer-matrix
calculations to determine a global phase diagram and also to proffer evidence
to check our prediction. | cond-mat_stat-mech |
Will jams get worse when slow cars move over?: Motivated by an analogy with traffic, we simulate two species of particles
(`vehicles'), moving stochastically in opposite directions on a two-lane ring
road. Each species prefers one lane over the other, controlled by a parameter
$0 \leq b \leq 1$ such that $b=0$ corresponds to random lane choice and $b=1$
to perfect `laning'. We find that the system displays one large cluster (`jam')
whose size increases with $b$, contrary to intuition. Even more remarkably, the
lane `charge' (a measure for the number of particles in their preferred lane)
exhibits a region of negative response: even though vehicles experience a
stronger preference for the `right' lane, more of them find themselves in the
`wrong' one! For $b$ very close to 1, a sharp transition restores a homogeneous
state. Various characteristics of the system are computed analytically, in good
agreement with simulation data. | cond-mat_stat-mech |
Multicomponent fluid of hard spheres near a wall: The rational function approximation method, density functional theory, and
NVT Monte Carlo simulation are used to obtain the density profiles of
multicomponent hard-sphere mixtures near a planar hard wall. Binary mixtures
with a size ratio 1:3 in which both components occupy a similar volume are
specifically examined. The results indicate that the present version of density
functional theory yields an excellent overall performance. A reasonably
accurate behavior of the rational function approximation method is also
observed, except in the vicinity of the first minimum, where it may even
predict unphysical negative values. | cond-mat_stat-mech |
Functional renormalization group approach to the dynamics of first-order
phase transitions: We apply the functional renormalization group theory to the dynamics of
first-order phase transitions and show that a potential with all odd-order
terms can describe spinodal decomposition phenomena. We derive a
momentum-dependent dynamic flow equation which is decoupled from the static
flow equation. We find the expected instability fixed points; and their
associated exponents agree remarkably with the existent theoretical and
numerical results. The complex renormalization group flows are found and their
properties are shown. Both the exponents and the complex flows show that the
spinodal decomposition possesses singularity with consequent scaling and
universality. | cond-mat_stat-mech |
Survival of an evasive prey: We study the survival of a prey that is hunted by N predators. The predators
perform independent random walks on a square lattice with V sites and start a
direct chase whenever the prey appears within their sighting range. The prey is
caught when a predator jumps to the site occupied by the prey. We analyze the
efficacy of a lazy, minimal-effort evasion strategy according to which the prey
tries to avoid encounters with the predators by making a hop only when any of
the predators appears within its sighting range; otherwise the prey stays
still. We show that if the sighting range of such a lazy prey is equal to 1
lattice spacing, at least 3 predators are needed in order to catch the prey on
a square lattice. In this situation, we establish a simple asymptotic relation
ln(Pev)(t) \sim (N/V)2ln(Pimm(t)) between the survival probabilities of an
evasive and an immobile prey. Hence, when the density of the predators is low
N/V<<1, the lazy evasion strategy leads to the spectacular increase of the
survival probability. We also argue that a short-sighting prey (its sighting
range is smaller than the sighting range of the predators) undergoes an
effective superdiffusive motion, as a result of its encounters with the
predators, whereas a far-sighting prey performs a diffusive-type motion. | cond-mat_stat-mech |
Geometric magnetism in classical transport theory: The effective dynamics of a slow classical system coupled to a fast chaotic
environment is described by means of a Master equation. We show how this
approach permits a very simple derivation of geometric magnetism. | cond-mat_stat-mech |
Anomalous scaling and large-scale anisotropy in magnetohydrodynamic
turbulence: Two-loop renormalization-group analysis of the
Kazantsev--Kraichnan kinematic model: The field theoretic renormalization group and operator product expansion are
applied to the Kazantsev--Kraichnan kinematic model for the magnetohydrodynamic
turbulence. The anomalous scaling emerges as a consequence of the existence of
certain composite fields ("operators") with negative dimensions. The anomalous
exponents for the correlation functions of arbitrary order are calculated in
the two-loop approximation (second order of the renormalization-group
expansion), including the anisotropic sectors. The anomalous scaling and the
hierarchy of anisotropic contributions become stronger due to those
second-order contributions. | cond-mat_stat-mech |
The non-Landauer Bound for the Dissipation of Bit Writing Operation: We propose a novel bound on the mimimum dissipation required in any
circumstances to transfer a certain amount of charge through any resistive
device. We illustrate it on the task of writing a logical 1 (encoded as a
prescribed voltage) into a capacitance, through various linear or nonlinear
devices. We show that, even though the celebrated Landauer bound (which only
applies to bit erasure) does not apply here, one can still formulate a "non-
Landauer" lower bound on dissipation, that crucially depends on the time budget
to perform the operation, as well as the average conductance of the driving
device. We compare our bound with empirical results reported in the literature
and realistic simulations of CMOS pass and transmission gates in decananometer
technology. Our non-Landauer bound turns out to be a quantitative benchmark to
assess the (non-)optimality of a writing operation. | cond-mat_stat-mech |
Emergent universal statistics in nonequilibrium systems with dynamical
scale selection: Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven
quantum matter and biological life forms to atmospheric and interstellar gases.
Identifying universal aspects of their far-from-equilibrium dynamics and
statistics poses major conceptual and practical challenges due to the absence
of energy and momentum conservation laws. Here, we experimentally and
theoretically investigate the statistics of prototypical nonequilibrium systems
in which inherent length-scale selection confines the dynamics near a mean
energy hypersurface. Guided by spectral analysis of the field modes and scaling
arguments, we derive a universal nonequilibrium distribution for kinetic field
observables. We confirm the predicted energy distributions in experimental
observations of Faraday surface waves, and in quantum chaos and active
turbulence simulations. Our results indicate that pattern dynamics and
transport in driven physical and biological matter can often be described
through monochromatic random fields, suggesting a path towards a unified
statistical field theory of nonequilibrium systems with length-scale selection. | cond-mat_stat-mech |
Effects of lengthscales and attractions on the collapse of hydrophobic
polymers in water: We present results from extensive molecular dynamics simulations of collapse
transitions of hydrophobic polymers in explicit water focused on understanding
effects of lengthscale of the hydrophobic surface and of attractive
interactions on folding. Hydrophobic polymers display parabolic, protein-like,
temperature-dependent free energy of unfolding. Folded states of small
attractive polymers are marginally stable at 300 K, and can be unfolded by
heating or cooling. Increasing the lengthscale or decreasing the polymer-water
attractions stabilizes folded states significantly, the former dominated by the
hydration contribution. That hydration contribution can be described by the
surface tension model, $\Delta G=\gamma (T)\Delta A$, where the surface
tension, $\gamma$, is lengthscale dependent and decreases monotonically with
temperature. The resulting variation of the hydration entropy with polymer
lengthscale is consistent with theoretical predictions of Huang and Chandler
(Proc. Natl. Acad. Sci.,97, 8324-8327, 2000) that explain the blurring of
entropy convergence observed in protein folding thermodynamics. Analysis of
water structure shows that the polymer-water hydrophobic interface is soft and
weakly dewetted, and is characterized by enhanced interfacial density
fluctuations. Formation of this interface, which induces polymer folding, is
strongly opposed by enthalpy and favored by entropy, similar to the
vapor-liquid interface. | cond-mat_stat-mech |
Logarithmically slow onset of synchronization: Here we investigate specifically the transient of a synchronizing system,
considering synchronization as a relaxation phenomenon. The stepwise
establishment of synchronization is studied in the system of dynamically
coupled maps introduced by Ito & Kaneko (Phys. Rev. Lett., 88, 028701, 2001 &
Phys. Rev. E, 67, 046226, 2003), where the plasticity of dynamical couplings
might be relevant in the context of neuroscience. We show the occurrence of
logarithmically slow dynamics in the transient of a fully deterministic
dynamical system. | cond-mat_stat-mech |
Growth of surfaces generated by a probabilistic cellular automaton: A one-dimensional cellular automaton with a probabilistic evolution rule can
generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete
models of surface growth are constructed from a probabilistic cellular
automaton which is known to show a transition from a active phase to a
absorbing phase at a critical probability associated with two particular
components of the evolution rule. In one of these models, called model $A$ in
this paper, the surface growth is defined in terms of the evolving front of the
cellular automaton on the space-time plane. In the other model, called model
$B$, surface growth takes place by a solid-on-solid deposition process
controlled by the cellular automaton configurations that appear in successive
time-steps. Both the models show a depinning transition at the critical point
of the generating cellular automaton. In addition, model $B$ shows a kinetic
roughening transition at this point. The characteristics of the surface width
in these models are derived by scaling arguments from the critical properties
of the generating cellular automaton and by Monte Carlo simulations. | cond-mat_stat-mech |
What is liquid? Lyapunov instability reveals symmetry-breaking
irreversibilities hidden within Hamilton's many-body equations of motion: Typical Hamiltonian liquids display exponential "Lyapunov instability", also
called "sensitive dependence on initial conditions". Although Hamilton's
equations are thoroughly time-reversible, the forward and backward Lyapunov
instabilities can differ, qualitatively. In numerical work, the expected
forward/backward pairing of Lyapunov exponents is also occasionally violated.
To illustrate, we consider many-body inelastic collisions in two space
dimensions. Two mirror-image colliding crystallites can either bounce, or not,
giving rise to a single liquid drop, or to several smaller droplets, depending
upon the initial kinetic energy and the interparticle forces. The difference
between the forward and backward evolutionary instabilities of these problems
can be correlated with dissipation and with the Second Law of Thermodynamics.
Accordingly, these asymmetric stabilities of Hamilton's equations can provide
an "Arrow of Time". We illustrate these facts for two small crystallites
colliding so as to make a warm liquid. We use a specially-symmetrized form of
Levesque and Verlet's bit-reversible Leapfrog integrator. We analyze
trajectories over millions of collisions with several equally-spaced time
reversals. | cond-mat_stat-mech |
Mechanisms of Carrier-Induced Ferromagnetism in Diluted Magnetic
Semiconductors: Two different approaches to the problem of carrier-induced ferromagnetism in
the system of the disordered magnetic ions, one bases on self-consistent
procedure for the exchange mean fields, other one bases on the RKKY
interaction, used in present literature as the alternative approximations is
analyzed. Our calculations in the framework of exactly solvable model show that
two different contributions to the magnetic characteristics of the system
represent these approaches. One stems from the diagonal part of carrier-ion
exchange interaction that corresponds to mean field approximation. Other one
stems from the off-diagonal part that describes the interaction between ion
spins via free carriers. These two contributions can be responsible for the
different magnetic properties, so aforementioned approaches are complementary,
not alternative. A general approach is proposed and compared with different
approximations to the problem under consideration. | cond-mat_stat-mech |
Corner transfer matrix renormalization group method for two-dimensional
self-avoiding walks and other O(n) models: We present an extension of the corner transfer matrix renormalisation group
(CTMRG) method to O(n) invariant models, with particular interest in the
self-avoiding walk class of models (O(n=0)). The method is illustrated using an
interacting self-avoiding walk model. Based on the efficiency and versatility
when compared to other available numerical methods, we present CTMRG as the
method of choice for two-dimensional self-avoiding walk problems. | cond-mat_stat-mech |
Non-hyperuniform metastable states around a disordered hyperuniform
state of densely packed spheres: stochastic density functional theory at
strong coupling: Disordered and hyperuniform structures of densely packed spheres near and at
jamming are characterized by vanishing of long-wavelength density fluctuations,
or equivalently by long-range power-law decay of the direct correlation
function (DCF). We focus on previous simulation results that exhibit
degradation of hyperuniformity in jammed structures while maintaining the
long-range nature of the DCF to a certain length scale. Here we demonstrate
that a field-theoretic formulation of the stochastic density functional theory
is relevant to explore the degradation mechanism. The strong-coupling expansion
method of the stochastic density functional theory is developed to obtain the
metastable chemical potential considering intermittent fluctuations in dense
packings. The metastable chemical potential yields an analytical form of the
metastable DCF that has a short-range cutoff inside the sphere while retaining
the long-range power-law behavior. It is confirmed that the metastable DCF
provides zero-wavevector limit of structure factor in quantitative agreement
with the previous simulation results of degraded hyperuniformity. We can also
predict the emergence of soft modes localized at the particle scale from
plugging this metastable DCF into the linearized Dean-Kawasaki equation, a
stochastic density functional equation. | cond-mat_stat-mech |
Virtual potentials for feedback traps: The recently developed feedback trap can be used to create arbitrary virtual
potentials, to explore the dynamics of small particles or large molecules in
complex situations. Experimentally, feedback traps introduce several finite
time scales: there is a delay between the measurement of a particle's position
and the feedback response; the feedback response is applied for a finite update
time; and a finite camera exposure integrates motion. We show how to
incorporate such timing effects into the description of particle motion. For
the test case of a virtual quadratic potential, we give the first accurate
description of particle dynamics, calculating the power spectrum and variance
of fluctuations as a function of feedback gain, testing against simulations. We
show that for small feedback gains, the motion approximates that of a particle
in an ordinary harmonic potential. Moreover, if the potential is varied in
time, for example by varying its stiffness, the work that is calculated
approximates that done in an ordinary changing potential. The quality of the
approximation is set by the ratio of the update time of the feedback loop to
the relaxation time of motion in the virtual potential. | cond-mat_stat-mech |
Entanglement transitions as a probe of quasiparticles and quantum
thermalization: We introduce a diagnostic for quantum thermalization based on mixed-state
entanglement. Specifically, given a pure state on a tripartite system $ABC$, we
study the scaling of entanglement negativity between $A$ and $B$. For
representative states of self-thermalizing systems, either eigenstates or
states obtained by a long-time evolution of product states, negativity shows a
sharp transition from an area-law scaling to a volume-law scaling when the
subsystem volume fraction is tuned across a finite critical value. In contrast,
for a system with quasiparticles, it exhibits a volume-law scaling irrespective
of the subsystem fraction. For many-body localized systems, the same quantity
shows an area-law scaling for eigenstates, and volume-law scaling for long-time
evolved product states, irrespective of the subsystem fraction. We provide a
combination of numerical observations and analytical arguments in support of
our conjecture. Along the way, we prove and utilize a `continuity bound' for
negativity: we bound the difference in negativity for two density matrices in
terms of the Hilbert-Schmidt norm of their difference. | cond-mat_stat-mech |
Stochastic Turing Patterns for systems with one diffusing species: The problem of pattern formation in a generic two species reaction--diffusion
model is studied, under the hypothesis that only one species can diffuse. For
such a system, the classical Turing instability cannot take place. At variance,
by working in the generalized setting of a stochastic formulation to the
inspected problem, Turing like patterns can develop, seeded by finite size
corrections. General conditions are given for the stochastic Turing patterns to
occur. The predictions of the theory are tested for a specific case study. | cond-mat_stat-mech |
Obtaining pressure versus concentration phase diagrams in spin systems
from Monte Carlo simulations: We propose an efficient procedure for determining phase diagrams of systems
that are described by spin models. It consists of combining cluster algorithms
with the method proposed by Sauerwein and de Oliveira where the grand canonical
potential is obtained directly from the Monte Carlo simulation, without the
necessity of performing numerical integrations. The cluster algorithm presented
in this paper eliminates metastability in first order phase transitions
allowing us to locate precisely the first-order transitions lines. We also
produce a different technique for calculating the thermodynamic limit of
quantities such as the magnetization whose infinite volume limit is not
straightforward in first order phase transitions. As an application, we study
the Andelman model for Langmuir monolayers made of chiral molecules that is
equivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained the
phase diagrams in the case where the intermolecular forces favor interactions
between enantiomers of the same type (homochiral interactions). In particular,
we have determined diagrams in the surface pressure versus concentration plane
which are more relevant from the experimental point of view and less usual in
numerical studies. | cond-mat_stat-mech |
Decoupling of self-diffusion and structural relaxation during a
fragile-to-strong crossover in a kinetically constrained lattice gas: We present an interpolated kinetically constrained lattice gas model which
exhibits a transition from fragile to strong supercooled liquid behavior. We
find non-monotonic decoupling that is due to this crossover and is seen in
experiment. | cond-mat_stat-mech |
Universality Class of Discrete Solid-on-Solid Limited Mobility
Nonequilibrium Growth Models for Kinetic Surface Roughening: We investigate, using the noise reduction technique, the asymptotic
universality class of the well-studied nonequilibrium limited mobility
atomistic solid-on-solid surface growth models introduced by Wolf and Villain
(WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface
roughening in ideal molecular beam epitaxy. We find essentially all the earlier
conclusions regarding the universality class of DT and WV models to be severely
hampered by slow crossover and extremely long lived transient effects. We
identify the correct asymptotic universality class(es) which differs from
earlier conclusions in several instances. | cond-mat_stat-mech |
Hurst Exponents, Markov Processes, and Fractional Brownian motion: There is much confusion in the literature over Hurst exponents. Recently, we
took a step in the direction of eliminating some of the confusion. One purpose
of this paper is to illustrate the difference between fBm on the one hand and
Gaussian Markov processes where H not equal to 1/2 on the other. The difference
lies in the increments, which are stationary and correlated in one case and
nonstationary and uncorrelated in the other. The two- and one-point densities
of fBm are constructed explicitly. The two-point density doesn't scale. The
one-point density is identical with that for a Markov process with H not 1/2.
We conclude that both Hurst exponents and histograms for one point densities
are inadequate for deducing an underlying stochastic dynamical system from
empirical data. | cond-mat_stat-mech |
Decision Making in the Arrow of Time: We show that the steady-state entropy production rate of a stochastic process
is inversely proportional to the minimal time needed to decide on the direction
of the arrow of time. Here we apply Wald's sequential probability ratio test to
optimally decide on the direction of time's arrow in stationary Markov
processes. Furthermore the steady state entropy production rate can be
estimated using mean first-passage times of suitable physical variables. We
derive a first-passage time fluctuation theorem which implies that the decision
time distributions for correct and wrong decisions are equal. Our results are
illustrated by numerical simulations of two simple examples of nonequilibrium
processes. | cond-mat_stat-mech |
Stretch diffusion and heat conduction in 1D nonlinear lattices: In the study of 1D nonlinear Hamiltonian lattices, the conserved quantities
play an important role in determining the actual behavior of heat conduction.
Besides the total energy, total momentum and total stretch could also be
conserved quantities. In microcanonical Hamiltonian dynamics, the total energy
is always conserved. It was recently argued by Das and Dhar that whenever
stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and
energy fields exhibit normal diffusion. In this work, we will systematically
investigate the stretch diffusions for typical 1D nonlinear lattices. No clear
connection between the conserved quantities and heat conduction can be
established. The actual situation is more complicated than what Das and Dhar
claimed. | cond-mat_stat-mech |
Kinetic theory of discontinuous shear thickening for a dilute gas-solid
suspension: A kinetic theory for a dilute gas-solid suspension under a simple shear is
developed. With the aid of the corresponding Boltzmann equation, it is found
that the flow curve (stress-strain rate relation) has a S-shape as a crossover
from the Newtonian to the Bagnoldian for a granular suspension or from the
Newtonian to a fluid having a viscosity proportional to the square of the shear
rate for a suspension consisting of elastic particles. The existence of the
S-shape in the flow curve directly leads to a discontinuous shear thickening
(DST). This DST corresponds to the discontinuous transition of the kinetic
temperature between a quenched state and an ignited state. The results of the
event-driven Langevin simulation of hard spheres perfectly agree with the
theoretical results without any fitting parameter. The simulation confirms that
the DST takes place in the linearly unstable region of the uniformly sheared
state. | cond-mat_stat-mech |
Low temperature thermodynamics of inverse square spin models in one
dimension: We present a field-theoretic renormalization group calculation in two loop
order for classical O(N)-models with an inverse square interaction in the
vicinity of their lower critical dimensionality one. The magnetic
susceptibility at low temperatures is shown to diverge like $T^{-a} \exp(b/T)$
with $a=(N-2)/(N-1)$ and $b=2\pi^2/(N-1)$. From a comparison with the exactly
solvable Haldane-Shastry model we find that the same temperature dependence
applies also to ferromagnetic quantum spin chains. | cond-mat_stat-mech |
Geometric magnetism in open quantum systems: An isolated classical chaotic system, when driven by the slow change of
several parameters, responds with two reaction forces: geometric friction and
geometric magnetism. By using the theory of quantum fluctuation relations we
show that this holds true also for open quantum systems, and provide explicit
expressions for those forces in this case. This extends the concept of Berry
curvature to the realm of open quantum systems. We illustrate our findings by
calculating the geometric magnetism of a damped charged quantum harmonic
oscillator transported along a path in physical space in presence of a magnetic
field and a thermal environment. We find that in this case the geometric
magnetism is unaffected by the presence of the heat bath. | cond-mat_stat-mech |
Critical curves in conformally invariant statistical systems: We consider critical curves -- conformally invariant curves that appear at
critical points of two-dimensional statistical mechanical systems. We show how
to describe these curves in terms of the Coulomb gas formalism of conformal
field theory (CFT). We also provide links between this description and the
stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the
long-time limit of stochastic evolution of various SLE observables related to
CFT primary fields. We show how the multifractal spectrum of harmonic measure
and other fractal characteristics of critical curves can be obtained. | cond-mat_stat-mech |
Phase Transitions and Scaling in Systems Far From Equilibrium: Scaling ideas and renormalization group approaches proved crucial for a deep
understanding and classification of critical phenomena in thermal equilibrium.
Over the past decades, these powerful conceptual and mathematical tools were
extended to continuous phase transitions separating distinct non-equilibrium
stationary states in driven classical and quantum systems. In concordance with
detailed numerical simulations and laboratory experiments, several prominent
dynamical universality classes have emerged that govern large-scale, long-time
scaling properties both near and far from thermal equilibrium. These pertain to
genuine specific critical points as well as entire parameter space regions for
steady states that display generic scale invariance. The exploration of
non-stationary relaxation properties and associated physical aging scaling
constitutes a complementary potent means to characterize cooperative dynamics
in complex out-of-equilibrium systems. This article describes dynamic scaling
features through paradigmatic examples that include near-equilibrium critical
dynamics, driven lattice gases and growing interfaces, correlation-dominated
reaction-diffusion systems, and basic epidemic models. | cond-mat_stat-mech |
Metastability in Markov processes: We present a formalism to describe slowly decaying systems in the context of
finite Markov chains obeying detailed balance. We show that phase space can be
partitioned into approximately decoupled regions, in which one may introduce
restricted Markov chains which are close to the original process but do not
leave these regions. Within this context, we identify the conditions under
which the decaying system can be considered to be in a metastable state.
Furthermore, we show that such metastable states can be described in
thermodynamic terms and define their free energy. This is accomplished showing
that the probability distribution describing the metastable state is indeed
proportional to the equilibrium distribution, as is commonly assumed. We test
the formalism numerically in the case of the two-dimensional kinetic Ising
model, using the Wang--Landau algorithm to show this proportionality
explicitly, and confirm that the proportionality constant is as derived in the
theory. Finally, we extend the formalism to situations in which a system can
have several metastable states. | cond-mat_stat-mech |
Exact Large Deviations of the Current in the Asymmetric Simple Exclusion
Process with Open Boundaries: In this thesis, we consider one of the most popular models of non-equilibrium
statistical physics: the Asymmetric Simple Exclusion Process, in which
particles jump stochastically on a one-dimensional lattice, between two
reservoirs at fixed densities, with the constraint that each site can hold at
most one particle at a given time. This model has the mathematical property of
being integrable, which makes it a good candidate for exact calculations. What
interests us in particular is the current of particles that flows through the
system (which is a sign of it being out of equilibrium), and how it fluctuates
with time. We present a method, based on the "matrix Ansatz" devised by
Derrida, Evans, Hakim and Pasquier, that allows to access the exact cumulants
of that current, for any finite size of the system and any value of its
parameters. We also analyse the large size asymptotics of our result, and make
a conjecture for the phase diagram of the system in the so-called "s-ensemble".
Finally, we show how our method relates to the algebraic Bethe Ansatz, which
was thought not to be applicable to this situation. | cond-mat_stat-mech |
Critical Casimir Forces for Films with Bulk Ordering Fields: The confinement of long-ranged critical fluctuations in the vicinity of
second-order phase transitions in fluids generates critical Casimir forces
acting on confining surfaces or among particles immersed in a critical solvent.
This is realized in binary liquid mixtures close to their consolute point
$T_{c}$ which belong to the universality class of the Ising model. The
deviation of the difference of the chemical potentials of the two species of
the mixture from its value at criticality corresponds to the bulk magnetic
filed of the Ising model. By using Monte Carlo simulations for this latter
representative of the corresponding universality class we compute the critical
Casimir force as a function of the bulk ordering field at the critical
temperature $T=T_{c}$. We use a coupling parameter scheme for the computation
of the underlying free energy differences and an energy-magnetization
integration method for computing the bulk free energy density which is a
necessary ingredient. By taking into account finite-size corrections, for
various types of boundary conditions we determine the universal Casimir force
scaling function as a function of the scaling variable associated with the bulk
field. Our numerical data are compared with analytic results obtained from
mean-field theory. | cond-mat_stat-mech |
Point processes in arbitrary dimension from fermionic gases, random
matrix theory, and number theory: It is well known that one can map certain properties of random matrices,
fermionic gases, and zeros of the Riemann zeta function to a unique point
process on the real line. Here we analytically provide exact generalizations of
such a point process in d-dimensional Euclidean space for any d, which are
special cases of determinantal processes. In particular, we obtain the
n-particle correlation functions for any n, which completely specify the point
processes. We also demonstrate that spin-polarized fermionic systems have these
same n-particle correlation functions in each dimension. The point processes
for any d are shown to be hyperuniform. The latter result implies that the pair
correlation function tends to unity for large pair distances with a decay rate
that is controlled by the power law r^[-(d+1)]. We graphically display one- and
two-dimensional realizations of the point processes in order to vividly reveal
their "repulsive" nature. Indeed, we show that the point processes can be
characterized by an effective "hard-core" diameter that grows like the square
root of d. The nearest-neighbor distribution functions for these point
processes are also evaluated and rigorously bounded. Among other results, this
analysis reveals that the probability of finding a large spherical cavity of
radius r in dimension d behaves like a Poisson point process but in dimension
d+1 for large r and finite d. We also show that as d increases, the point
process behaves effectively like a sphere packing with a coverage fraction of
space that is no denser than 1/2^d. | cond-mat_stat-mech |
Generalized thermodynamic uncertainty relations: We analyze ensemble in which energy (E), temperature (T) and multiplicity (N)
can all fluctuate and with the help of nonextensive statistics we propose a
relation connecting all fluctuating variables. It generalizes Lindhard's
thermodynamic uncertainty relations known in literature. | cond-mat_stat-mech |
Critical Phenomena and Renormalization-Group Theory: We review results concerning the critical behavior of spin systems at
equilibrium. We consider the Ising and the general O($N$)-symmetric
universality classes, including the $N\to 0$ limit that describes the critical
behavior of self-avoiding walks. For each of them, we review the estimates of
the critical exponents, of the equation of state, of several amplitude ratios,
and of the two-point function of the order parameter. We report results in
three and two dimensions. We discuss the crossover phenomena that are observed
in this class of systems. In particular, we review the field-theoretical and
numerical studies of systems with medium-range interactions. Moreover, we
consider several examples of magnetic and structural phase transitions, which
are described by more complex Landau-Ginzburg-Wilson Hamiltonians, such as
$N$-component systems with cubic anisotropy, O($N$)-symmetric systems in the
presence of quenched disorder, frustrated spin systems with noncollinear or
canted order, and finally, a class of systems described by the tetragonal
Landau-Ginzburg-Wilson Hamiltonian with three quartic couplings. The results
for the tetragonal Hamiltonian are original, in particular we present the
six-loop perturbative series for the $\beta$-functions. Finally, we consider a
Hamiltonian with symmetry $O(n_1)\oplus O(n_2)$ that is relevant for the
description of multicritical phenomena. | cond-mat_stat-mech |
Harnessing symmetry to control quantum transport: Controlling transport in quantum systems holds the key to many promising
quantum technologies. Here we review the power of symmetry as a resource to
manipulate quantum transport, and apply these ideas to engineer novel quantum
devices. Using tools from open quantum systems and large deviation theory, we
show that symmetry-mediated control of transport is enabled by a pair of twin
dynamic phase transitions in current statistics, accompanied by a coexistence
of different transport channels. By playing with the symmetry decomposition of
the initial state, one can modulate the importance of the different transport
channels and hence control the flowing current. Motivated by the problem of
energy harvesting we illustrate these ideas in open quantum networks, an
analysis which leads to the design of a symmetry-controlled quantum thermal
switch. We review an experimental setup recently proposed for symmetry-mediated
quantum control in the lab based on a linear array of atom-doped optical
cavities, and the possibility of using transport as a probe to uncover hidden
symmetries, as recently demonstrated in molecular junctions, is also discussed.
Other symmetry-mediated control mechanisms are also described. Overall, these
results demonstrate the importance of symmetry not only as an organizing
principle in physics but also as a tool to control quantum systems. | cond-mat_stat-mech |
Two dimensional XXZ-Ising model on square-hexagon lattice: We study a two dimensional XXZ-Ising on square-hexagon (4-6) lattice with
spin-1/2. The phase diagram of the ground state energy is discussed, shown two
different ferrimagnetic states and two type of antiferromagnetic states, beside
of a ferromagnetic state. To solve this model, it could be mapped into the
eight-vertex model with union jack interaction term. Imposing exact solution
condition we find the region where the XXZ-Ising model on 4-6 lattice have
exact solutions with one free parameter, for symmetric eight-vertex model
condition. In this sense we explore the properties of the system and analyze
the competition of the interaction parameters providing the region where it has
an exact solution. However the present model does not satisfy the \textit{free
fermion} condition, unless for a trivial situation. Even so we are able to
discuss their critical points region, when the exactly solvable condition is
ignored. | cond-mat_stat-mech |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.