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Quantitative field theory of the glass transition: We develop a full microscopic replica field theory of the dynamical
transition in glasses. By studying the soft modes that appear at the dynamical
temperature we obtain an effective theory for the critical fluctuations. This
analysis leads to several results: we give expressions for the mean field
critical exponents, and we study analytically the critical behavior of a set of
four-points correlation functions from which we can extract the dynamical
correlation length. Finally, we can obtain a Ginzburg criterion that states the
range of validity of our analysis. We compute all these quantities within the
Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find
results that are consistent with numerical simulations. | cond-mat_dis-nn |
Critical indices of Anderson transition: something is wrong with
numerical results: Numerical results for Anderson transition are critically discussed. A simple
procedure to deal with corrections to scaling is suggested. With real
uncertainties taken into account, the raw data are in agreement with a value
$\nu=1$ for the critical index of the correlation length in three dimensions. | cond-mat_dis-nn |
A Generalized Rate Model for Neuronal Ensembles: There has been a long-standing controversy whether information in neuronal
networks is carried by the firing rate code or by the firing temporal code. The
current status of the rivalry between the two codes is briefly reviewed with
the recent studies such as the brain-machine interface (BMI). Then we have
proposed a generalized rate model based on the {\it finite} $N$-unit Langevin
model subjected to additive and/or multiplicative noises, in order to
understand the firing property of a cluster containing $N$ neurons. The
stationary property of the rate model has been studied with the use of the
Fokker-Planck equation (FPE) method. Our rate model is shown to yield various
kinds of stationary distributions such as the interspike-interval distribution
expressed by non-Gaussians including gamma, inverse-Gaussian-like and
log-normal-like distributions.
The dynamical property of the generalized rate model has been studied with
the use of the augmented moment method (AMM) which was developed by the author
[H. Hasegawa, J. Phys. Soc. Jpn. 75 (2006) 033001]. From the macroscopic point
of view in the AMM, the property of the $N$-unit neuron cluster is expressed in
terms of {\it three} quantities; $\mu$, the mean of spiking rates of $R=(1/N)
\sum_i r_i$ where $r_i$ denotes the firing rate of a neuron $i$ in the cluster:
$\gamma$, averaged fluctuations in local variables ($r_i$): $\rho$,
fluctuations in global variable ($R$). We get equations of motions of the three
quantities, which show $\rho \sim \gamma/N$ for weak couplings. This implies
that the population rate code is generally more reliable than the single-neuron
rate code. Our rate model is extended and applied to an ensemble containing
multiple neuron clusters. | cond-mat_dis-nn |
Statistical Properties of Ideal Ensemble of Disordered 1D Steric
Spin-Chains: The statistical properties of ensemble of disordered 1D steric spin-chains
(SSC) of various length are investigated. Using 1D spin-glass type classical
Hamiltonian, the recurrent trigonometrical equations for stationary points and
corresponding conditions for the construction of stable 1D SSCs are found. The
ideal ensemble of spin-chains is analyzed and the latent interconnections
between random angles and interaction constants for each set of three
nearest-neighboring spins are found. It is analytically proved and by numerical
calculation is shown that the interaction constant satisfies L\'{e}vy's
alpha-stable distribution law. Energy distribution in ensemble is calculated
depending on different conditions of possible polarization of spin-chains. It
is specifically shown that the dimensional effects in the form of set of local
maximums in the energy distribution arise when the number of spin-chains M <<
N_x^2 (where N_x is number of spins in a chain) while in the case when M ~
N_x^2 energy distribution has one global maximum and ensemble of spin-chains
satisfies Birkhoff's ergodic theorem. Effective algorithm for parallel
simulation of problem which includes calculation of different statistic
parameters of 1D SSCs ensemble is elaborated. | cond-mat_dis-nn |
Mean field treatment of exclusion processes with random-force disorder: The asymmetric simple exclusion process with random-force disorder is studied
within the mean field approximation. The stationary current through a domain
with reversed bias is analyzed and the results are found to be in accordance
with earlier intuitive assumptions. On the grounds of these results, a
phenomenological random barrier model is applied in order to describe
quantitatively the coarsening phenomena. Predictions of the theory are compared
with numerical results obtained by integrating the mean field evolution
equations. | cond-mat_dis-nn |
Statistical Properties of the one dimensional Anderson model relevant
for the Nonlinear Schrödinger Equation in a random potential: The statistical properties of overlap sums of groups of four eigenfunctions
of the Anderson model for localization as well as combinations of four
eigenenergies are computed. Some of the distributions are found to be scaling
functions, as expected from the scaling theory for localization. These enable
to compute the distributions in regimes that are otherwise beyond the
computational resources. These distributions are of great importance for the
exploration of the Nonlinear Schr\"odinger Equation (NLSE) in a random
potential since in some explorations the terms we study are considered as noise
and the present work describes its statistical properties. | cond-mat_dis-nn |
Antiferromagnetic effects in Chaotic Map lattices with a conservation
law: Some results about phase separation in coupled map lattices satisfying a
conservation law are presented. It is shown that this constraint is the origin
of interesting antiferromagnetic effective couplings and allows transitions to
antiferromagnetic and superantiferromagnetic phases. Similarities and
differences between this models and statistical spin models are pointed out. | cond-mat_dis-nn |
Disordered and ordered states of exactly solvable Ising-Heisenberg
planar models with a spatial anisotropy: Ground-state and finite-temperature properties of a special class of exactly
solvable Ising-Heisenberg planar models are examined using the generalized
decoration-iteration and star-triangle mapping transformations. The
investigated spin systems exhibit an interesting quantum behaviour manifested
in a remarkable geometric spin frustration, which appears notwithstanding the
purely ferromagnetic interactions of the considered model systems. This kind of
spin frustration originates from an easy-plane anisotropy in the XXZ Heisenberg
interaction between nearest-neighbouring spins that favours ferromagnetic
ordering of their transverse components, whereas their longitudinal components
are aligned antiferomagnetically. | cond-mat_dis-nn |
Geometrical organization of solutions to random linear Boolean equations: The random XORSAT problem deals with large random linear systems of Boolean
variables. The difficulty of such problems is controlled by the ratio of number
of equations to number of variables. It is known that in some range of values
of this parameter, the space of solutions breaks into many disconnected
clusters. Here we study precisely the corresponding geometrical organization.
In particular, the distribution of distances between these clusters is computed
by the cavity method. This allows to study the `x-satisfiability' threshold,
the critical density of equations where there exist two solutions at a given
distance. | cond-mat_dis-nn |
Random sequential adsorption of shrinking or spreading particles: We present a model of one-dimensional irreversible adsorption in which
particles once adsorbed immediately shrink to a smaller size or expand to a
larger size. Exact solutions for the fill factor and the particle number
variance as a function of the size change are obtained. Results are compared
with approximate analytical solutions. | cond-mat_dis-nn |
Anomalous Roughening in Experiments of Interfaces in Hele-Shaw Flows
with Strong Quenched Disorder: We report experimental evidences of anomalous kinetic roughening in the
stable displacement of an oil-air interface in a Hele-Shaw cell with strong
quenched disorder. The disorder consists on a random modulation of the gap
spacing transverse to the growth direction (tracks). We have performed
experiments varying average interface velocity and gap spacing, and measured
the scaling exponents. We have obtained beta=0.50, beta*=0.25, alpha=1.0,
alpha_l=0.5, and z=2. When there is no fluid injection, the interface is driven
solely by capillary forces, and a higher value of beta around beta=0.65 is
measured. The presence of multiscaling and the particular morphology of the
interfaces, characterized by high slopes that follow a L\'evy distribution,
confirms the existence of anomalous scaling. From a detailed study of the
motion of the oil--air interface we show that the anomaly is a consequence of
different local velocities over tracks plus the coupling in the motion between
neighboring tracks. The anomaly disappears at high interface velocities, weak
capillary forces, or when the disorder is not sufficiently persistent in the
growth direction. We have also observed the absence of scaling when the
disorder is very strong or when a regular modulation of the gap spacing is
introduced. | cond-mat_dis-nn |
On the mechanical beta relaxation in glass and its relation to the
double-peak phenomenon in impulse excited vibration at high temperatures: A viscoelastic model is established to reveal the relation between alpha-beta
relaxation of glass and the double-peak phenomenon in the experiments of
impulse excited vibration. In the modelling, the normal mode analysis (NMA) of
potential energy landscape (PEL) picture is employed to describe mechanical
alpha and beta relaxations in a glassy material. The model indicates that a
small beta relaxation can lead to an apparent double-peak phenomenon resulted
from the free vibration of a glass beam when the frequency of beta relaxation
peak is close to the natural frequency of specimen. The theoretical prediction
is validated by the acoustic spectrum of a fluorosilicate glass beam excited by
a mid-span impulse. Furthermore, the experimental results indicate a negative
temperature-dependence of the frequency of beta relaxation in the
fluorosilicate glass S-FSL5 which can be explained based on the physical
picture of fragmented oxide-network patches in liquid-like regions. | cond-mat_dis-nn |
Dependence of critical parameters of 2D Ising model on lattice size: For the 2D Ising model, we analyzed dependences of thermodynamic
characteristics on number of spins by means of computer simulations. We
compared experimental data obtained using the Fisher-Kasteleyn algorithm on a
square lattice with $N=l{\times}l$ spins and the asymptotic Onsager solution
($N\to\infty$). We derived empirical expressions for critical parameters as
functions of $N$ and generalized the Onsager solution on the case of a
finite-size lattice. Our analytical expressions for the free energy and its
derivatives (the internal energy, the energy dispersion and the heat capacity)
describe accurately the results of computer simulations. We showed that when
$N$ increased the heat capacity in the critical point increased as $lnN$. We
specified restrictions on the accuracy of the critical temperature due to
finite size of our system. Also in the finite-dimensional case, we obtained
expressions describing temperature dependences of the magnetization and the
correlation length. They are in a good qualitative agreement with the results
of computer simulations by means of the dynamic Metropolis Monte Carlo method. | cond-mat_dis-nn |
k-Core percolation on multiplex networks: We generalize the theory of k-core percolation on complex networks to k-core
percolation on multiplex networks, where k=(k_a, k_b, ...). Multiplex networks
can be defined as networks with a set of vertices but different types of edges,
a, b, ..., representing different types of interactions. For such networks, the
k-core is defined as the largest sub-graph in which each vertex has at least
k_i edges of each type, i = a, b, ... . We derive self-consistency equations to
obtain the birth points of the k-cores and their relative sizes for
uncorrelated multiplex networks with an arbitrary degree distribution. To
clarify our general results, we consider in detail multiplex networks with
edges of two types, a and b, and solve the equations in the particular case of
ER and scale-free multiplex networks. We find hybrid phase transitions at the
emergence points of k-cores except the (1,1)-core for which the transition is
continuous. We apply the k-core decomposition algorithm to air-transportation
multiplex networks, composed of two layers, and obtain the size of (k_a,
k_b)-cores. | cond-mat_dis-nn |
The replica symmetric region in the Sherrington-Kirkpatrick mean field
spin glass model. The Almeida-Thouless line: In previous work, we have developed a simple method to study the behavior of
the Sherrington-Kirkpatrick mean field spin glass model for high temperatures,
or equivalently for high external fields. The basic idea was to couple two
different replicas with a quadratic term, trying to push out the two replica
overlap from its replica symmetric value. In the case of zero external field,
our results reproduced the well known validity of the annealed approximation,
up to the known critical value for the temperature. In the case of nontrivial
external field, our method could prove the validity of the
Sherrington-Kirkpatrick replica symmetric solution up to a line, which fell
short of the Almeida-Thouless line, associated to the onset of the spontaneous
replica symmetry breaking, in the Parisi Ansatz. Here, we make a strategic
improvement of the method, by modifying the flow equations, with respect to the
parameters of the model. We exploit also previous results on the overlap
fluctuations in the replica symmetric region. As a result, we give a simple
proof that replica symmetry holds up to the critical Almeida-Thouless line, as
expected on physical grounds. Our results are compared with the
characterization of the replica symmetry breaking line previously given by
Talagrand. We outline also a possible extension of our methods to the broken
replica symmetry region. | cond-mat_dis-nn |
Liquid markets and market liquids: collective and single-asset dynamics
in financial markets: We characterize the collective phenomena of a liquid market. By interpreting
the behavior of a no-arbitrage N asset market in terms of a particle system
scenario, (thermo)dynamical-like properties can be extracted from the asset
kinetics. In this scheme the mechanisms of the particle interaction can be
widely investigated. We test the verisimilitude of our construction on
two-decade stock market daily data (DAX30) and show the result obtained for the
interaction potential among asset pairs. | cond-mat_dis-nn |
A Mean-field Approach for an Intercarrier Interference Canceller for
OFDM: The similarity of the mathematical description of random-field spin systems
to orthogonal frequency-division multiplexing (OFDM) scheme for wireless
communication is exploited in an intercarrier-interference (ICI) canceller used
in the demodulation of OFDM. The translational symmetry in the Fourier domain
generically concentrates the major contribution of ICI from each subcarrier in
the subcarrier's neighborhood. This observation in conjunction with mean field
approach leads to a development of an ICI canceller whose necessary cost of
computation scales linearly with respect to the number of subcarriers. It is
also shown that the dynamics of the mean-field canceller are well captured by a
discrete map of a single macroscopic variable, without taking the spatial and
time correlations of estimated variables into account. | cond-mat_dis-nn |
Statistical Design of Chaotic Waveforms with Enhanced Targeting
Capabilities: We develop a statistical theory of waveform shaping of incident waves that
aim to efficiently deliver energy at weakly lossy targets which are embedded
inside chaotic enclosures. Our approach utilizes the universal features of
chaotic scattering -- thus minimizing the use of information related to the
exact characteristics of the chaotic enclosure. The proposed theory applies
equally well to systems with and without time-reversal symmetry. | cond-mat_dis-nn |
Critical behavior of a cellular automaton highway traffic model: We derive the critical behavior of a CA traffic flow model using an order
parameter breaking the symmetry of the jam-free phase. Random braking appears
to be the symmetry-breaking field conjugate to the order parameter. For
$v_{\max}=2$, we determine the values of the critical exponents $\beta$,
$\gamma$ and $\delta$ using an order-3 cluster approximation and computer
simulations. These critical exponents satisfy a scaling relation, which can be
derived assuming that the order parameter is a generalized homogeneous function
of $|\rho-\rho_c|$ and p in the vicinity of the phase transition point. | cond-mat_dis-nn |
Entropy of complex relevant components of Boolean networks: Boolean network models of strongly connected modules are capable of capturing
the high regulatory complexity of many biological gene regulatory circuits. We
study numerically the previously introduced basin entropy, a parameter for the
dynamical uncertainty or information storage capacity of a network as well as
the average transient time in random relevant components as a function of their
connectivity. We also demonstrate that basin entropy can be estimated from
time-series data and is therefore also applicable to non-deterministic networks
models. | cond-mat_dis-nn |
The metastable minima of the Heisenberg spin glass in a random magnetic
field: We have studied zero temperature metastable states in classical $m$-vector
component spin glasses in the presence of $m$-component random fields (of
strength $h_{r}$) for a variety of models, including the Sherrington
Kirkpatrick (SK) model, the Viana Bray (VB) model and the randomly diluted
one-dimensional models with long-range power law interactions. For the SK model
we have calculated analytically its complexity (the log of the number of
minima) for both the annealed case and the quenched case, both for fields above
and below the de Almeida Thouless (AT) field ($h_{AT} > 0$ for $m>2$). We have
done quenches starting from a random initial state by putting spins parallel to
their local fields until convergence and found that in zero field it always
produces minima which have zero overlap with each other. For the $m=2$ and
$m=3$ cases in the SK model the final energy reached in the quench is very
close to the energy $E_c$ at which the overlap of the states would acquire
replica symmetry breaking features. These minima have marginal stability and
will have long-range correlations between them. In the SK limit we have
analytically studied the density of states $\rho(\lambda)$ of the Hessian
matrix in the annealed approximation. Despite the absence of continuous
symmetries, the spectrum extends down to zero with the usual $\sqrt{\lambda}$
form for the density of states for $h_{r}<h_{AT}$. However, when
$h_{r}>h_{AT}$, there is a gap in the spectrum which closes up as $h_{AT}$ is
approached. For the VB model and the other models our numerical work shows that
there always exist some low-lying eigenvalues and there never seems to be a
gap. There is no sign of the AT transition in the quenched states reached from
infinite temperature for any model but the SK model, which is the only model
which has zero complexity above $h_{AT}$. | cond-mat_dis-nn |
A theoretical model of neuronal population coding of stimuli with both
continuous and discrete dimensions: In a recent study the initial rise of the mutual information between the
firing rates of N neurons and a set of p discrete stimuli has been analytically
evaluated, under the assumption that neurons fire independently of one another
to each stimulus and that each conditional distribution of firing rates is
gaussian. Yet real stimuli or behavioural correlates are high-dimensional, with
both discrete and continuously varying features.Moreover, the gaussian
approximation implies negative firing rates, which is biologically implausible.
Here, we generalize the analysis to the case where the stimulus or behavioural
correlate has both a discrete and a continuous dimension. In the case of large
noise we evaluate the mutual information up to the quadratic approximation as a
function of population size. Then we consider a more realistic distribution of
firing rates, truncated at zero, and we prove that the resulting correction,
with respect to the gaussian firing rates, can be expressed simply as a
renormalization of the noise parameter. Finally, we demonstrate the effect of
averaging the distribution across the discrete dimension, evaluating the mutual
information only with respect to the continuously varying correlate. | cond-mat_dis-nn |
Cascading Parity-Check Error-Correcting Codes: A method for improving the performance of sparse-matrix based parity check
codes is proposed, based on insight gained from methods of statistical physics.
The advantages of the new approach are demonstrated on an existing
encoding/decoding paradigm suggested by Sourlas. We also discuss the
application of the same method to more advanced codes of a similar type. | cond-mat_dis-nn |
Absorbing phase transitions in a non-conserving sandpile model: We introduce and study a non-conserving sandpile model, the autonomously
adapting sandpile (AAS) model, for which a site topples whenever it has two or
more grains, distributing three or two grains randomly on its neighboring
sites, respectively with probability $p$ and $(1-p)$. The toppling process is
independent of the actual number of grains $z_i$ of the toppling site, as long
as $z_i\ge2$. For a periodic lattice the model evolves into an inactive state
for small $p$, with the number of active sites becoming stationary for larger
values of $p$. In one and two dimensions we find that the absorbing phase
transition occurs for $p_c\!\approx\!0.717$ and $p_c\!\approx\!0.275$.
The symmetry of bipartite lattices allows states in which all active sites
are located alternatingly on one of the two sublattices, A and B, respectively
for even and odd times. We show that the AB-sublattice symmetry is
spontaneously broken for the AAS model, an observation that holds also for the
Manna model. One finds that a metastable AB-symmetry conserving state is
transiently observable and that it has the potential to influence the width of
the scaling regime, in particular in two dimensions.
The AAS model mimics the behavior of integrate-and-fire neurons which
propagate activity independently of the input received, as long as the
threshold is crossed. Abstracting from regular lattices, one can identify sites
with neurons and consider quenched networks of neurons connected to a fixed
number $G$ of other neurons, with $G$ being drawn from a suitable distribution.
The neuronal activity is then propagated to $G$ other neurons. The AAS model is
hence well suited for theoretical studies of nearly critical brain dynamics. We
also point out that the waiting-time distribution allows an avalanche-free
experimental access to criticality. | cond-mat_dis-nn |
Single crystal growth and study of the magnetic properties of the mixed
spin-dimer system Ba$_{3-x}$Sr$_{x}$Cr$_{2}$O$_{8}$: The compounds Sr$_{3}$Cr$_{2}$O$_{8}$ and Ba$_{3}$Cr$_{2}$O$_{8}$ are
insulating dimerized antiferromagnets with Cr$^{5+}$ magnetic ions. These
spin-$\frac{1}{2}$ ions form hexagonal bilayers with a strong intradimer
antiferromagnetic interaction, that leads to a singlet ground state and gapped
triplet states. We report on the effect on the magnetic properties of
Sr$_{3}$Cr$_{2}$O$_{8}$ by introducing chemical disorder upon replacing Sr by
Ba. Two single crystals of Ba$_{3-x}$Sr$_{x}$Cr$_{2}$O$_{8}$ with $x=2.9$
(3.33\% of $mixing$) and $x=2.8$ (6.66\%) were grown in a four-mirror type
optical floating-zone furnace. The magnetic properties on these compounds were
studied by magnetization measurements. Inelastic neutron scattering
measurements on Ba$_{0.1}$Sr$_{2.9}$Cr$_{2}$O$_{8}$ were performed in order to
determine the interaction constants and the spin gap for $x=2.9$. The
intradimer interaction constant is found to be $J_0$=5.332(2) meV, about 4\%
smaller than that of pure Sr$_{3}$Cr$_{2}$O$_{8}$, while the interdimer
exchange interaction $J_e$ is smaller by 6.9\%. These results indicate a
noticeable change in the magnetic properties by a random substitution effect. | cond-mat_dis-nn |
Selberg integrals in 1D random Euclidean optimization problems: We consider a set of Euclidean optimization problems in one dimension, where
the cost function associated to the couple of points $x$ and $y$ is the
Euclidean distance between them to an arbitrary power $p\ge1$, and the points
are chosen at random with flat measure. We derive the exact average cost for
the random assignment problem, for any number of points, by using Selberg's
integrals. Some variants of these integrals allows to derive also the exact
average cost for the bipartite travelling salesman problem. | cond-mat_dis-nn |
Inflation versus projection sets in aperiodic systems: The role of the
window in averaging and diffraction: Tilings based on the cut and project method are key model systems for the
description of aperiodic solids. Typically, quantities of interest in
crystallography involve averaging over large patches, and are well defined only
in the infinite-volume limit. In particular, this is the case for
autocorrelation and diffraction measures. For cut and project systems, the
averaging can conveniently be transferred to internal space, which means
dealing with the corresponding windows. We illustrate this by the example of
averaged shelling numbers for the Fibonacci tiling and review the standard
approach to the diffraction for this example. Further, we discuss recent
developments for inflation-symmetric cut and project structures, which are
based on an internal counterpart of the renormalisation cocycle. Finally, we
briefly review the notion of hyperuniformity, which has recently gained
popularity, and its application to aperiodic structures. | cond-mat_dis-nn |
The complex dynamics of memristive circuits: analytical results and
universal slow relaxation: Networks with memristive elements (resistors with memory) are being explored
for a variety of applications ranging from unconventional computing to models
of the brain. However, analytical results that highlight the role of the graph
connectivity on the memory dynamics are still a few, thus limiting our
understanding of these important dynamical systems. In this paper, we derive an
exact matrix equation of motion that takes into account all the network
constraints of a purely memristive circuit, and we employ it to derive
analytical results regarding its relaxation properties. We are able to describe
the memory evolution in terms of orthogonal projection operators onto the
subspace of fundamental loop space of the underlying circuit. This orthogonal
projection explicitly reveals the coupling between the spatial and temporal
sectors of the memristive circuits and compactly describes the circuit
topology. For the case of disordered graphs, we are able to explain the
emergence of a power law relaxation as a superposition of exponential
relaxation times with a broad range of scales using random matrices. This power
law is also {\it universal}, namely independent of the topology of the
underlying graph but dependent only on the density of loops. In the case of
circuits subject to alternating voltage instead, we are able to obtain an
approximate solution of the dynamics, which is tested against a specific
network topology. These result suggest a much richer dynamics of memristive
networks than previously considered. | cond-mat_dis-nn |
Spin Glasses: An introduction and overview is given of the theory of spin glasses and its
application. | cond-mat_dis-nn |
Spatio-temporal correlations in Wigner molecules: The dynamical response of Coulomb-interacting particles in nano-clusters are
analyzed at different temperatures characterizing their solid- and liquid-like
behavior. Depending on the trap-symmetry, both the spatial and temporal
correlations undergo slow, stretched exponential relaxations at long times,
arising from spatially correlated motion in string-like paths. Our results
indicate that the distinction between the `solid' and `liquid' is soft: While
particles in a `solid' flow producing dynamic heterogeneities, motion in
`liquid' yields unusually long tail in the distribution of
particle-displacements. A phenomenological model captures much of the
subtleties of our numerical simulations. | cond-mat_dis-nn |
Phase Ordering and Onset of Collective Behavior in Chaotic Coupled Map
Lattices: The phase ordering properties of lattices of band-chaotic maps coupled
diffusively with some coupling strength $g$ are studied in order to determine
the limit value $g_e$ beyond which multistability disappears and non-trivial
collective behavior is observed. The persistence of equivalent discrete spin
variables and the characteristic length of the patterns observed scale
algebraically with time during phase ordering. The associated exponents vary
continuously with $g$ but remain proportional to each other, with a ratio close
to that of the time-dependent Ginzburg-Landau equation. The corresponding
individual values seem to be recovered in the space-continuous limit. | cond-mat_dis-nn |
Fate of Quadratic Band Crossing under quasiperiodic modulation: We study the fate of two-dimensional quadratic band crossing topological
phases under a one-dimensional quasiperiodic modulation. By employing
numerically exact methods, we fully characterize the phase diagram of the model
in terms of spectral, localization and topological properties. Unlike in the
presence of regular disorder, the quadratic band crossing is stable towards the
application of the quasiperiodic potential and most of the topological phase
transitions occur through a gap closing and reopening mechanism, as in the
homogeneous case. With a sufficiently strong quasiperiodic potential, the
quadratic band crossing point splits into Dirac cones which enables transitions
into gapped phases with Chern numbers $C=\pm1$, absent in the homogeneous
limit. This is in sharp contrast with the disordered case, where gapless
$C=\pm1$ phases can arise by perturbing the band crossing with any amount of
disorder. In the quasiperiodic case, we find that the $C=\pm1$ phases can only
become gapless for a very strong potential. Only in this regime, the subsequent
quasiperiodic-induced topological transitions into the trivial phase mirror the
well-known ``levitation and annihilation'' mechanism in the disordered case. | cond-mat_dis-nn |
Quantum Annealing: from Viewpoints of Statistical Physics, Condensed
Matter Physics, and Computational Physics: In this paper, we review some features of quantum annealing and related
topics from viewpoints of statistical physics, condensed matter physics, and
computational physics. We can obtain a better solution of optimization problems
in many cases by using the quantum annealing. Actually the efficiency of the
quantum annealing has been demonstrated for problems based on statistical
physics. Then the quantum annealing has been expected to be an efficient and
generic solver of optimization problems. Since many implementation methods of
the quantum annealing have been developed and will be proposed in the future,
theoretical frameworks of wide area of science and experimental technologies
will be evolved through studies of the quantum annealing. | cond-mat_dis-nn |
Power law hopping of single particles in one-dimensional non-Hermitian
quasicrystals: In this paper, a non-Hermitian Aubry-Andr\'e-Harper model with power-law
hoppings ($1/s^{a}$) and quasiperiodic parameter $\beta$ is studied, where $a$
is the power-law index, $s$ is the hopping distance, and $\beta$ is a member of
the metallic mean family. We find that under the weak non-Hermitian effect,
there preserves $P_{\ell=1,2,3,4}$ regimes where the fraction of ergodic
eigenstates is $\beta$-dependent as $\beta^{\ell}$L ($L$ is the system size)
similar to those in the Hermitian case. However, $P_{\ell}$ regimes are ruined
by the strong non-Hermitian effect. Moreover, by analyzing the fractal
dimension, we find that there are two types of edges aroused by the power-law
index $a$ in the single-particle spectrum, i.e., an ergodic-to-multifractal
edge for the long-range hopping case ($a<1$), and an ergodic-to-localized edge
for the short-range hopping case ($a>1$). Meanwhile, the existence of these two
types of edges is found to be robust against the non-Hermitian effect. By
employing the Simon-Spence theory, we analyzed the absence of the localized
states for $a<1$. For the short-range hopping case, with the Avila's global
theory and the Sarnak method, we consider a specific example with $a=2$ to
reveal the presence of the intermediate phase and to analytically locate the
intermediate regime and the ergodic-to-multifractal edge, which are
self-consistent with the numerically results. | cond-mat_dis-nn |
Universal spectral form factor for many-body localization: We theoretically study correlations present deep in the spectrum of
many-body-localized systems. An exact analytical expression for the spectral
form factor of Poisson spectra can be obtained and is shown to agree well with
numerical results on two models exhibiting many-body-localization: a disordered
quantum spin chain and a phenomenological $l$-bit model based on the existence
of local integrals of motion. We also identify a universal regime that is
insensitive to the global density of states as well as spectral edge effects. | cond-mat_dis-nn |
Wannier band transitions in disordered $π$-flux ladders: Boundary obstructed topological insulators are an unusual class of
higher-order topological insulators with topological characteristics determined
by the so-called Wannier bands. Boundary obstructed phases can harbor
hinge/corner modes, but these modes can often be destabilized by a phase
transition on the boundary instead of the bulk. While there has been much work
on the stability of topological insulators in the presence disorder, the
topology of a disordered Wannier band, and disorder-induced Wannier transitions
have not been extensively studied. In this work, we focus on the simplest
example of a Wannier topological insulator: a mirror-symmetric $\pi$-flux
ladder in 1D. We find that the Wannier topology is robust to disorder, and
derive a real-space renormalization group procedure to understand a new type of
strong disorder-induced transition between non-trivial and trivial Wannier
topological phases. We also establish a connection between the Wannier topology
of the ladder and the energy band topology of a related system with a physical
boundary cut, something which has generally been conjectured for clean models,
but has not been studied in the presence of disorder. | cond-mat_dis-nn |
Criticality and Chaos in Systems of Communities: We consider a simple model of communities interacting via bilinear terms.
After analyzing the thermal equilibrium case, which can be described by an
Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces
to a Glauber-like dynamics. We analyze and compare four different versions of
the dynamics: flow (differential equations), map (discrete-time dynamics),
local-time update flow, and local-time update map. The presence of only
bilinear interactions prevent the flow cases to develop any dynamical
instability, the system converging always to the thermal equilibrium. The
situation is different for the map when unfriendly couplings are involved,
where period-two oscillations arise. In the case of the map with local-time
updates, oscillations of any period and chaos can arise as a consequence of the
reciprocal "tension" accumulated among the communities during their sleeping
time interval. The resulting chaos can be of two kinds: true chaos
characterized by positive Lyapunov exponent and bifurcation cascades, or
marginal chaos characterized by zero Lyapunov exponent and critical continuous
regions. | cond-mat_dis-nn |
Simulation of multi-shell fullerenes using Machine-Learning Gaussian
Approximation Potential: Multi-shell fullerenes "buckyonions" were simulated, starting from initially
random configurations, using a density-functional-theory (DFT)-trained
machine-learning carbon potential within the Gaussian Approximation Potential
(ML-GAP) Framework [Volker L. Deringer and Gabor Csanyi, Phys. Rev. B 95,
094203 (2017)]. A large set of such fullerenes were obtained with sizes ranging
from 60 ~ 3774 atoms. The buckyonions are formed by clustering and layering
starts from the outermost shell and proceed inward. Inter-shell cohesion is
partly due to interaction between delocalized $\pi$ electrons into the gallery.
The energies of the models were validated ex post facto using density
functional codes, VASP and SIESTA, revealing an energy difference within the
range of 0.02 - 0.08 eV/atom after conjuagte gradient energy convergence of the
models were achieved with both methods. | cond-mat_dis-nn |
Context-dependent representation in recurrent neural networks: In order to assess the short-term memory performance of non-linear random
neural networks, we introduce a measure to quantify the dependence of a neural
representation upon the past context. We study this measure both numerically
and theoretically using the mean-field theory for random neural networks,
showing the existence of an optimal level of synaptic weights heterogeneity. We
further investigate the influence of the network topology, in particular the
symmetry of reciprocal synaptic connections, on this measure of context
dependence, revealing the importance of considering the interplay between
non-linearities and connectivity structure. | cond-mat_dis-nn |
Signatures of Many-Body Localization in the Dynamics of Two-Level
Systems in Glasses: We investigate the quantum dynamics of Two-Level Systems (TLS) in glasses at
low temperatures (1 K and below). We study an ensemble of TLSs coupled to
phonons. By integrating out the phonons within the framework of the
Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we derive
analytically the explicit form of the interactions among TLSs, and of the
dissipation terms. We find that the unitary dynamics of the system shows clear
signatures of Many-Body Localization physics. We study numerically the time
behavior of the concurrence, which measures pairwise entanglement also in
non-isolated systems, and show that it presents a power-law decay both in the
absence and in the presence of dissipation, if the latter is not too large.
These features can be ascribed to the strong, long-tailed disorder
characterizing the distributions of the model parameters. Our findings show
that assuming ergodicity when discussing TLS physics might not be justified for
all kinds of experiments on low-temperature glasses. | cond-mat_dis-nn |
Critical properties of the measurement-induced transition in random
quantum circuits: We numerically study the measurement-driven quantum phase transition of
Haar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite
mutual information we are able to make a precise estimate of the critical
measurement rate $p_c = 0.17(1)$. We extract estimates for the associated bulk
critical exponents that are consistent with the values for percolation, as well
as those for stabilizer circuits, but differ from previous estimates for the
Haar-random case. Our estimates of the surface order parameter exponent appear
different from that for stabilizer circuits or percolation, but we are unable
to definitively rule out the scenario where all exponents in the three cases
match. Moreover, in the Haar case the prefactor for the entanglement entropies
$S_n$ depends strongly on the R\'enyi index $n$; for stabilizer circuits and
percolation this dependence is absent. Results on stabilizer circuits are used
to guide our study and identify measures with weak finite-size effects. We
discuss how our numerical estimates constrain theories of the transition. | cond-mat_dis-nn |
On the Effects of Changing the Boundary Conditions on the Ground State
of Ising Spin Glasses: We compute and analyze couples of ground states of 3D spin glass systems with
the same quenched noise but periodic and anti-periodic boundary conditions for
different lattice sizes. We discuss the possible different behaviors of the
system, we analyze the average link overlap, the probability distribution of
window overlaps (among ground states computed with different boundary
conditions) and the spatial overlap and link overlap correlation functions. We
establish that the picture based on Replica Symmetry Breaking correctly
describes the behavior of 3D Spin Glasses. | cond-mat_dis-nn |
Comment on ``Both site and link overlap distributions are non trivial in
3-dimensional Ising spin glasses'', cond-mat/0608535v2: We comment on recent numerical experiments by G.Hed and E.Domany
[cond-mat/0608535v2] on the quenched equilibrium state of the Edwards-Anderson
spin glass model. The rigorous proof of overlap identities related to replica
equivalence shows that the observed violations of those identities on finite
size systems must vanish in the thermodynamic limit. See also the successive
version cond-mat/0608535v4 | cond-mat_dis-nn |
Intermittency of dynamical phases in a quantum spin glass: Answering the question of existence of efficient quantum algorithms for
NP-hard problems require deep theoretical understanding of the properties of
the low-energy eigenstates and long-time coherent dynamics in quantum spin
glasses. We discovered and described analytically the property of asymptotic
orthogonality resulting in a new type of structure in quantum spin glass. Its
eigen-spectrum is split into the alternating sequence of bands formed by
quantum states of two distinct types ($x$ and $z$). Those of $z$-type are
non-ergodic extended eigenstates (NEE) in the basis of $\{\sigma_z\}$ operators
that inherit the structure of the classical spin glass with exponentially long
decay times of Edwards Anderson order parameter at any finite value of
transverse field $B_{\perp}$. Those of $x$-type form narrow bands of NEEs that
conserve the integer-valued $x$-magnetization. Quantum evolution within a given
band of each type is described by a Hamiltonian that belongs to either the
ensemble of Preferred Basis Levi matrices ($z$-type) or Gaussian Orthogonal
ensemble ($x$-type). We characterize the non-equilibrium dynamics using fractal
dimension $D$ that depends on energy density (temperature) and plays a role of
thermodynamic potential: $D=0$ in MBL phase, $0<D<1$ in NEE phase,
$D\rightarrow 1$ in ergodic phase in infinite temperature limit. MBL states
coexist with NEEs in the same range of energies even at very large $B_{\perp}$.
Bands of NEE states can be used for new quantum search-like algorithms of
population transfer in the low-energy part of spin-configuration space.
Remarkably, the intermitted structure of the eigenspectrum emerges in quantum
version of a statistically featureless Random Energy Model and is expected to
exist in a class of paractically important NP-hard problems that unlike REM can
be implemented on a computer with polynomial resources. | cond-mat_dis-nn |
Infinite-disorder critical points of models with stretched exponential
interactions: We show that an interaction decaying as a stretched exponential function of
the distance, $J(l)\sim e^{-cl^a}$, is able to alter the universality class of
short-range systems having an infinite-disorder critical point. To do so, we
study the low-energy properties of the random transverse-field Ising chain with
the above form of interaction by a strong-disorder renormalization group (SDRG)
approach. We obtain that the critical behavior of the model is controlled by
infinite-disorder fixed points different from that of the short-range one if
$0<a<1/2$. In this range, the critical exponents calculated analytically by a
simplified SDRG scheme are found to vary with $a$, while, for $a>1/2$, the
model belongs to the same universality class as its short-range variant. The
entanglement entropy of a block of size $L$ increases logarithmically with $L$
in the critical point but, as opposed to the short-range model, the prefactor
is disorder-dependent in the range $0<a<1/2$. Numerical results obtained by an
improved SDRG scheme are found to be in agreement with the analytical
predictions. The same fixed points are expected to describe the critical
behavior of, among others, the random contact process with stretched
exponentially decaying activation rates. | cond-mat_dis-nn |
Fractal dimension of domain walls in two-dimensional Ising spin glasses: We study domain walls in 2d Ising spin glasses in terms of a minimum-weight
path problem. Using this approach, large systems can be treated exactly. Our
focus is on the fractal dimension $d_f$ of domain walls, which describes via
$<\ell >\simL^{d_f}$ the growth of the average domain-wall length with %%
systems size $L\times L$. %% 20.07.07 OM %% Exploring systems up to L=320 we
yield $d_f=1.274(2)$ for the case of Gaussian disorder, i.e. a much higher
accuracy compared to previous studies. For the case of bimodal disorder, where
many equivalent domain walls exist due to the degeneracy of this model, we
obtain a true lower bound $d_f=1.095(2)$ and a (lower) estimate $d_f=1.395(3)$
as upper bound. Furthermore, we study the distributions of the domain-wall
lengths. Their scaling with system size can be described also only by the
exponent $d_f$, i.e. the distributions are monofractal. Finally, we investigate
the growth of the domain-wall width with system size (``roughness'') and find a
linear behavior. | cond-mat_dis-nn |
Information propagation in isolated quantum systems: Entanglement growth and out-of-time-order correlators (OTOC) are used to
assess the propagation of information in isolated quantum systems. In this
work, using large scale exact time-evolution we show that for weakly disordered
nonintegrable systems information propagates behind a ballistically moving
front, and the entanglement entropy growths linearly in time. For stronger
disorder the motion of the information front is algebraic and sub-ballistic and
is characterized by an exponent which depends on the strength of the disorder,
similarly to the sublinear growth of the entanglement entropy. We show that the
dynamical exponent associated with the information front coincides with the
exponent of the growth of the entanglement entropy for both weak and strong
disorder. We also demonstrate that the temporal dependence of the OTOC is
characterized by a fast\emph onnonexponential\emph default growth, followed by
a slow saturation after the passage of the information front. Finally,we
discuss the implications of this behavioral change on the growth of the
entanglement entropy. | cond-mat_dis-nn |
The unreasonable effectiveness of tree-based theory for networks with
clustering: We demonstrate that a tree-based theory for various dynamical processes
yields extremely accurate results for several networks with high levels of
clustering. We find that such a theory works well as long as the mean
intervertex distance $\ell$ is sufficiently small - i.e., as long as it is
close to the value of $\ell$ in a random network with negligible clustering and
the same degree-degree correlations. We confirm this hypothesis numerically
using real-world networks from various domains and on several classes of
synthetic clustered networks. We present analytical calculations that further
support our claim that tree-based theories can be accurate for clustered
networks provided that the networks are "sufficiently small" worlds. | cond-mat_dis-nn |
Energy transport in a disordered spin chain with broken U(1) symmetry:
Diffusion, subdiffusion, and many-body localization: We explore the physics of the disordered XYZ spin chain using two
complementary numerical techniques: exact diagonalization (ED) on chains of up
to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400
spins. Our principal findings are as follows. First, the clean XYZ spin chain
shows ballistic energy transport for all parameter values that we investigated.
Second, for weak disorder there is a stable diffusive region that persists up
to a critical disorder strength that depends on the XY anisotropy. Third, for
disorder strengths above this critical value energy transport becomes
increasingly subdiffusive. Fourth, the many-body localization transition moves
to significantly higher disorder strengths as the XY anisotropy is increased.
We discuss these results, and their relation to our current physical picture of
subdiffusion in the approach to many-body localization. | cond-mat_dis-nn |
Competitive cluster growth in complex networks: Understanding the process by which the individuals of a society make up their
minds and reach opinions about different issues can be of fundamental
importance. In this work we propose an idealized model for competitive cluster
growth in complex networks. Each cluster can be thought as a fraction of a
community that shares some common opinion. Our results show that the cluster
size distribution depends on the particular choice for the topology of the
network of contacts among the agents. As an application, we show that the
cluster size distributions obtained when the growth process is performed on
hierarchical networks, e.g., the Apollonian network, have a scaling form
similar to what has been observed for the distribution of number of votes in an
electoral process. We suggest that this similarity is due to the fact that
social networks involved in the electoral process may also posses an
underlining hierarchical structure. | cond-mat_dis-nn |
Classical magnetotransport of inhomogeneous conductors: We present a model of magnetotransport of inhomogeneous conductors based on
an array of coupled four-terminal elements. We show that this model generically
yields non-saturating magnetoresistance at large fields. We also discuss how
this approach simplifies finite-element analysis of bulk inhomogeneous
semiconductors in complex geometries. We argue that this is an explanation of
the observed non-saturating magnetoresistance in silver chalcogenides and
potentially in other disordered conductors. Our method may be used to design
the magnetoresistive response of a microfabricated array. | cond-mat_dis-nn |
Phase Diagram of mixed bond Ising systems by use of Monte Carlo and the
effective-field theory: The phase transition of a random mixed-bond Ising ferromagnet on a cubic
lattice model is studied both numerically and analytically. In this work, we
use the Cluster algorithms of Wolff and Glauber to simulate the dynamics of the
system. We obtained the thermodynamic quantities such as magnetization,
susceptibility, and specific heat. Our results were compared with those
obtained using a new technique in effective field theory that employs similar
probability distribution within the framework of two-site clusters | cond-mat_dis-nn |
Statistics of energy levels and eigenfunctions in disordered and chaotic
systems: Supersymmetry approach: The supersymmetry method has proven to be a very powerful tool of study of
the statistical properties of energy levels and eigenfunctions in disordered
and chaotic systems. The aim of these lectures is to present a tutorial
introduction to the method, as well as an overview of the recent developments. | cond-mat_dis-nn |
Improved algorithm for neuronal ensemble inference by Monte Carlo method: Neuronal ensemble inference is one of the significant problems in the study
of biological neural networks. Various methods have been proposed for ensemble
inference from their activity data taken experimentally. Here we focus on
Bayesian inference approach for ensembles with generative model, which was
proposed in recent work. However, this method requires large computational
cost, and the result sometimes gets stuck in bad local maximum solution of
Bayesian inference. In this work, we give improved Bayesian inference algorithm
for these problems. We modify ensemble generation rule in Markov chain Monte
Carlo method, and introduce the idea of simulated annealing for hyperparameter
control. We also compare the performance of ensemble inference between our
algorithm and the original one. | cond-mat_dis-nn |
Molecular neuron based on the Franck-Condon blockade: Electronic realizations of neurons are of great interest as building blocks
for neuromorphic computation. Electronic neurons should send signals into the
input and output lines when subject to an input signal exceeding a given
threshold, in such a way that they may affect all other parts of a neural
network. Here, we propose a design for a neuron that is based on
molecular-electronics components and thus promises a very high level of
integration. We employ the Monte Carlo technique to simulate typical time
evolutions of this system and thereby show that it indeed functions as a
neuron. | cond-mat_dis-nn |
Apparent slow dynamics in the ergodic phase of a driven many-body
localized system without extensive conserved quantities: We numerically study the dynamics on the ergodic side of the many-body
localization transition in a periodically driven Floquet model with no global
conservation laws. We describe and employ a numerical technique based on the
fast Walsh-Hadamard transform that allows us to perform an exact time evolution
for large systems and long times. As in models with conserved quantities (e.g.,
energy and/or particle number) we observe a slowing down of the dynamics as the
transition into the many-body localized phase is approached. More specifically,
our data is consistent with a subballistic spread of entanglement and a
stretched-exponential decay of an autocorrelation function, with their
associated exponents reflecting slow dynamics near the transition for a fixed
system size. However, with access to larger system sizes, we observe a clear
flow of the exponents towards faster dynamics and can not rule out that the
slow dynamics is a finite-size effect. Furthermore, we observe examples of
non-monotonic dependence of the exponents with time, with dynamics initially
slowing down but accelerating again at even larger times, consistent with the
slow dynamics being a crossover phenomena with a localized critical point. | cond-mat_dis-nn |
One step replica symmetry breaking and overlaps between two temperatures: We obtain an exact analytic expression for the average distribution, in the
thermodynamic limit, of overlaps between two copies of the same random energy
model (REM) at different temperatures. We quantify the non-self averaging
effects and provide an exact approach to the computation of the fluctuations in
the distribution of overlaps in the thermodynamic limit. We show that the
overlap probabilities satisfy recurrence relations that generalise
Ghirlanda-Guerra identities to two temperatures.
We also analyse the two temperature REM using the replica method. The replica
expressions for the overlap probabilities satisfy the same recurrence relations
as the exact form. We show how a generalisation of Parisi's replica symmetry
breaking ansatz is consistent with our replica expressions. A crucial aspect to
this generalisation is that we must allow for fluctuations in the replica block
sizes even in the thermodynamic limit. This contrasts with the single
temperature case where the extremal condition leads to a fixed block size in
the thermodynamic limit. Finally, we analyse the fluctuations of the block
sizes in our generalised Parisi ansatz and show that in general they may have a
negative variance. | cond-mat_dis-nn |
A conjectured scenario for order-parameter fluctuations in spin glasses: We study order-parameter fluctuations (OPF) in disordered systems by
considering the behavior of some recently introduced paramaters $G,G_c$ which
have proven very useful to locate phase transitions. We prove that both
parameters G (for disconnected overlap disorder averages) and $G_c$ (for
connected disorder averages) take the respective universal values 1/3 and 13/31
in the $T\to 0$ limit for any {\em finite} volume provided the ground state is
{\em unique} and there is no gap in the ground state local-field distributions,
conditions which are met in generic spin-glass models with continuous couplings
and no gap at zero coupling. This makes $G,G_c$ ideal parameters to locate
phase transitions in disordered systems much alike the Binder cumulant is for
ordered systems. We check our results by exactly computing OPF in a simple
example of uncoupled spins in the presence of random fields and the
one-dimensional Ising spin glass. At finite temperatures, we discuss in which
conditions the value 1/3 for G may be recovered by conjecturing different
scenarios depending on whether OPF are finite or vanish in the infinite-volume
limit. In particular, we discuss replica equivalence and its natural
consequence $\lim_{V\to\infty}G(V,T)=1/3$ when OPF are finite. As an example of
a model where OPF vanish and replica equivalence does not give information
about G we study the Sherrington-Kirkpatrick spherical spin-glass model by
doing numerical simulations for small sizes. Again we find results compatible
with G=1/3 in the spin-glass phase. | cond-mat_dis-nn |
Experimental study of the effect of disorder on subcritical crack growth
dynamics: The growth dynamics of a single crack in a heterogeneous material under
subcritical loading is an intermittent process; and many features of this
dynamics have been shown to agree with simple models of thermally activated
rupture. In order to better understand the role of material heterogeneities in
this process, we study the subcritical propagation of a crack in a sheet of
paper in the presence of a distribution of small defects such as holes. The
experimental data obtained for two different distributions of holes are
discussed in the light of models that predict the slowing down of crack growth
when the disorder in the material is increased; however, in contradiction with
these theoretical predictions, the experiments result in longer lasting cracks
in a more ordered scenario. We argue that this effect is specific to
subcritical crack dynamics and that the weakest zones between holes at close
distance to each other are responsible both for the acceleration of the crack
dynamics and the slightly different roughness of the crack path. | cond-mat_dis-nn |
A statistical-mechanical approach to CDMA multiuser detection:
propagating beliefs in a densely connected graph: The task of CDMA multiuser detection is to simultaneously estimate binary
symbols of $K$ synchronous users from the received $N$ base-band CDMA signals.
Mathematically, this can be formulated as an inference problem on a complete
bipartite graph. In the research on graphically represented statistical models,
it is known that the belief propagation (BP) can exactly perform the inference
in a polynomial time scale of the system size when the graph is free from
cycles in spite that the necessary computation for general graphs exponentially
explodes in the worst case. In addition, recent several researches revealed
that the BP can also serve as an excellent approximation algorithm even if the
graph has cycles as far as they are relatively long. However, as there exit
many short cycles in a complete bipartite graph, one might suspect that the BP
would not provide a good performance when employed for the multiuser detection.
The purpose of this paper is to make an objection to such suspicion. More
specifically, we will show that appropriate employment of the central limit
theorem and the law of large numbers to BP, which is one of the standard
techniques in statistical mechanics, makes it possible to develop a novel
multiuser detection algorithm the convergence property of which is considerably
better than that of the conventional multistage detection without increasing
the computational cost significantly. Furthermore, we will also provide a
scheme to analyse the dynamics of the proposed algorithm, which can be
naturally linked to the equilibrium analysis recently presented by Tanaka. | cond-mat_dis-nn |
Chemical order lifetimes in liquids in the energy landscape paradigm: Recent efforts to deal with the complexities of the liquid state,
particularly those of glassforming systems, have focused on the "energy
landscape" as a means of dealing with the collective variables problem [1]. The
"basins of attraction" that constitute the landscape features in configuration
space represent a distinct class of microstates of the system. So far only the
microstates that are related to structural relaxation and viscosity have been
considered in this paradigm. But most of the complex systems of importance in
nature and industry are solutions, particularly solutions that are highly
non-ideal in character. In these, a distinct class of fluctuations exists, the
fluctuations in concentration. The mean square amplitudes of these fluctuations
relate to the chemical activity coefficients [2], and their rise and decay
times may be much longer than those of the density fluctuations - from which
they may be statistically independent. Here we provide data on the character of
chemical order fluctuations in viscous liquids and on their relation to the
enthalpy fluctuations that determine the structural relaxation time, and hence
the glass temperature Tg. Using a spectroscopically active chemical order
probe, we identify a "chemical fictive temperature", Tchm, by analogy with the
familiar "fictive temperature" Tf (the cooling Tg). Like Tf, Tchm must be the
same as the real temperature for the system to be in complete equilibrium. It
is possible for mobile multicomponent liquids to be permanently nonergodic,
insofar as Tchm > Tf = T, which must be accommodated within the landscape
paradigm. We note that, in appropriate systems, an increase in concentration of
slow chemically ordering units in liquids can produce a crossover to fast ion
conducting glass phenomenology. | cond-mat_dis-nn |
Analytic Solution to Clustering Coefficients on Weighted Networks: Clustering coefficient is an important topological feature of complex
networks. It is, however, an open question to give out its analytic expression
on weighted networks yet. Here we applied an extended mean-field approach to
investigate clustering coefficients in the typical weighted networks proposed
by Barrat, Barth\'elemy and Vespignani (BBV networks). We provide analytical
solutions of this model and find that the local clustering in BBV networks
depends on the node degree and strength. Our analysis is well in agreement with
results of numerical simulations. | cond-mat_dis-nn |
Water Droplet Avalanches: We analyze the statistics of water droplet avalanches in a continuously
driven system. Distributions are obtained for avalanche size, lifetime, and
time between successive avalanches, along with power spectra and return maps.
For low flow rates and different water viscosities, we observe a power-law
scaling in the size and lifetime distributions of water droplet avalanches,
indicating that a state with no characteristic time and length scales was
reached. Higher flow rates resulted in an exponential behavior with
characteristic scales. | cond-mat_dis-nn |
Structural and Energetic Heterogeneity in Protein Folding: A general theoretical framework is developed using free energy functional
methods to understand the effects of heterogeneity in the folding of a
well-designed protein. Native energetic heterogeneity arising from
non-uniformity in native stability, as well as entropic heterogeneity intrinsic
to the topology of the native structure are both investigated as to their
impact on the folding free energy landscape and resulting folding mechanism.
Given a minimally frustrated protein, both structural and energetic
heterogeneity lower the thermodynamic barrier to folding, and designing in
sufficient heterogeneity can eliminate the barrier at the folding transition
temperature. Sequences with different distributions of stability throughout the
protein and correspondingly different folding mechanisms may still be good
folders to the same structure. This theoretical framework allows for a
systematic study of the coupled effects of energetics and topology in protein
folding, and provides interpretations and predictions for future experiments
which may investigate these effects. | cond-mat_dis-nn |
Spin-charge separation and many-body localization: We study many-body localization for a disordered chain of spin 1/2 fermions.
In [Phys. Rev. B \textbf{94}, 241104 (2016)], when both down and up components
are exposed to the same strong disorder, the authors observe a power law growth
of the entanglement entropy that suggests that many-body localization is not
complete; the density (charge) degree of freedom is localized, while the spin
degree of freedom is apparently delocalized. We show that this power-like
behavior is only a transient effect and that, for longer times, the growth is
logarithmic in time suggesting that the spin degree of freedom is also
localized, so that the system follows the standard many-body localization
scenario. We also study the experimentally relevant case of quasiperiodic
disorder. | cond-mat_dis-nn |
Stretched Exponential Relaxation on the Hypercube and the Glass
Transition: We study random walks on the dilute hypercube using an exact enumeration
Master equation technique, which is much more efficient than Monte Carlo
methods for this problem. For each dilution $p$ the form of the relaxation of
the memory function $q(t)$ can be accurately parametrized by a stretched
exponential $q(t)=\exp(-(t/\tau)^\beta)$ over several orders of magnitude in
$q(t)$. As the critical dilution for percolation $p_c$ is approached, the time
constant $\tau(p)$ tends to diverge and the stretching exponent $\beta(p)$
drops towards 1/3. As the same pattern of relaxation is observed in wide class
of glass formers, the fractal like morphology of the giant cluster in the
dilute hypercube is a good representation of the coarse grained phase space in
these systems. For these glass formers the glass transition can be pictured as
a percolation transition in phase space. | cond-mat_dis-nn |
Exciton Dephasing and Thermal Line Broadening in Molecular Aggregates: Using a model of Frenkel excitons coupled to a bath of acoustic phonons in
the host medium, we study the temperature dependence of the dephasing rates and
homogeneous line width in linear molecular aggregates. The model includes
localization by disorder and predicts a power-law thermal scaling of the
effective homogeneous line width. The theory gives excellent agreement with
temperature dependent absorption and hole-burning experiments on aggregates of
the dye pseudoisocyanine. | cond-mat_dis-nn |
Aging dynamics of ferromagnetic and reentrant spin glass phases in
stage-2 Cu$_{0.80}$C$_{0.20}$Cl$_{2}$ graphite intercalation compound: Aging dynamics of a reentrant ferromagnet stage-2
Cu$_{0.8}$Co$_{0.2}$Cl$_{2}$ graphite intercalation compound has been studied
using DC magnetic susceptibility. This compound undergoes successive
transitions at the transition temperatures $T_{c}$ ($\approx 8.7$ K) and
$T_{RSG}$ ($\approx 3.3$ K). The relaxation rate $S_{ZFC}(t)$ exhibits a
characteristic peak at $t_{cr}$ below $T_{c}$. The peak time $t_{cr}$ as a
function of temperature $T$ shows a local maximum around 5.5 K, reflecting a
frustrated nature of the ferromagnetic phase. It drastically increases with
decreasing temperature below $T_{RSG}$. The spin configuration imprinted at the
stop and wait process at a stop temperature $T_{s}$ ($<T_{c}$) during the
field-cooled aging protocol, becomes frozen on further cooling. On reheating,
the memory of the aging at $T_{s}$ is retrieved as an anomaly of the
thermoremnant magnetization at $T_{s}$. These results indicate the occurrence
of the aging phenomena in the ferromagnetic phase ($T_{RSG}<T<T_{c}$) as well
as in the reentrant spin glass phase ($T<T_{RSG}$). | cond-mat_dis-nn |
A Mutual Attraction Model for Both Assortative and Disassortative
Weighted Networks: In most networks, the connection between a pair of nodes is the result of
their mutual affinity and attachment. In this letter, we will propose a Mutual
Attraction Model to characterize weighted evolving networks. By introducing the
initial attractiveness $A$ and the general mechanism of mutual attraction
(controlled by parameter $m$), the model can naturally reproduce scale-free
distributions of degree, weight and strength, as found in many real systems.
Simulation results are in consistent with theoretical predictions.
Interestingly, we also obtain nontrivial clustering coefficient C and tunable
degree assortativity r, depending on $m$ and A. Our weighted model appears as
the first one that unifies the characterization of both assortative and
disassortative weighted networks. | cond-mat_dis-nn |
Langevin description of speckle dynamics in nonlinear disordered media: We formulate a Langevin description of dynamics of a speckle pattern
resulting from the multiple scattering of a coherent wave in a nonlinear
disordered medium. The speckle pattern exhibits instability with respect to
periodic excitations at frequencies $\Omega$ below some
$\Omega_{\mathrm{max}}$, provided that the nonlinearity exceeds some
$\Omega$-dependent threshold. A transition of the speckle pattern from a
stationary state to the chaotic evolution is predicted upon increasing
nonlinearity. The shortest typical time scale of chaotic intensity fluctuations
is of the order of $1/\Omega_\mathrm {max}$. | cond-mat_dis-nn |
Specific-Heat Exponent of Random-Field Systems via Ground-State
Calculations: Exact ground states of three-dimensional random field Ising magnets (RFIM)
with Gaussian distribution of the disorder are calculated using
graph-theoretical algorithms. Systems for different strengths h of the random
fields and sizes up to N=96^3 are considered. By numerically differentiating
the bond-energy with respect to h a specific-heat like quantity is obtained,
which does not appear to diverge at the critical point but rather exhibits a
cusp. We also consider the effect of a small uniform magnetic field, which
allows us to calculate the T=0 susceptibility. From a finite-size scaling
analysis, we obtain the critical exponents \nu=1.32(7), \alpha=-0.63(7),
\eta=0.50(3) and find that the critical strength of the random field is
h_c=2.28(1). We discuss the significance of the result that \alpha appears to
be strongly negative. | cond-mat_dis-nn |
Machine learning the dynamics of quantum kicked rotor: Using the multilayer convolutional neural network (CNN), we can detect the
quantum phases in random electron systems, and phase diagrams of two and higher
dimensional Anderson transitions and quantum percolations as well as disordered
topological systems have been obtained. Here, instead of using CNN to analyze
the wave functions, we analyze the dynamics of wave packets via long short-term
memory network (LSTM). We adopt the quasi-periodic quantum kicked rotors, which
simulate the three and four dimensional Anderson transitions. By supervised
training, we let LSTM extract the features of the time series of wave packet
displacements in localized and delocalized phases. We then simulate the wave
packets in unknown phases and let LSTM classify the time series to localized
and delocalized phases. We compare the phase diagrams obtained by LSTM and
those obtained by CNN. | cond-mat_dis-nn |
Flat-band-based multifractality in the all-band-flat diamond chain: We study the effect of quasiperiodic Aubry-Andr\'e disorder on the energy
spectrum and eigenstates of a one-dimensional all-bands-flat (ABF) diamond
chain. The ABF diamond chain possesses three dispersionless flat bands with all
the eigenstates compactly localized on two unit cells in the zero disorder
limit. The fate of the compact localized states in the presence of the disorder
depends on the symmetry of the applied potential. We consider two cases here: a
symmetric one, where the same disorder is applied to the top and bottom sites
of a unit cell and an antisymmetric one, where the disorder applied to the top
and bottom sites are of equal magnitude but with opposite signs. Remarkably,
the symmetrically perturbed lattice preserves compact localization, although
the degeneracy is lifted. When the lattice is perturbed antisymmetrically, not
only is the degeneracy is lifted but compact localization is also destroyed.
Fascinatingly, all eigenstates exhibit a multifractal nature below a critical
strength of the applied potential. A central band of eigenstates continue to
display an extended yet non-ergodic behaviour for arbitrarily large strengths
of the potential. All other eigenstates exhibit the familiar Anderson
localization above the critical potential strength. We show how the
antisymmetric disordered model can be mapped to a $\frac{\pi}{4}$ rotated
square lattice with nearest and selective next-nearest neighbour hopping and a
staggered magnetic field - such models have been shown to exhibit
multifractality. Surprisingly, the antisymmetric disorder (with an even number
of unit cells) preserves chiral symmetry - we show this by explicitly writing
down the chiral operator. | cond-mat_dis-nn |
Sznajd Complex Networks: The Sznajd cellular automata corresponds to one of the simplest and yet most
interesting models of complex systems. While the traditional two-dimensional
Sznajd model tends to a consensus state (pro or cons), the assignment of the
contrary to the dominant opinion to some of its cells during the system
evolution is known to provide stabilizing feedback implying the overall system
state to oscillate around null magnetization. The current article presents a
novel type of geographic complex network model whose connections follow an
associated feedbacked Sznajd model, i.e. the Sznajd dynamics is run over the
network edges. Only connections not exceeding a maximum Euclidean distance $D$
are considered, and any two nodes within such a distance are randomly selected
and, in case they are connected, all network nodes which are no further than
$D$ are connected to them. In case they are not connected, all nodes within
that distance are disconnected from them. Pairs of nodes are then randomly
selected and assigned to the contrary of the dominant connectivity. The
topology of the complex networks obtained by such a simple growth scheme, which
are typically characterized by patches of connected communities, is analyzed
both at global and individual levels in terms of a set of hierarchical
measurements introduced recently. A series of interesting properties are
identified and discussed comparatively to random and scale-free models with the
same number of nodes and similar connectivity. | cond-mat_dis-nn |
Renormalization group analysis of the random first order transition: We consider the approach describing glass formation in liquids as a
progressive trapping in an exponentially large number of metastable states. To
go beyond the mean-field setting, we provide a real-space renormalization group
(RG) analysis of the associated replica free-energy functional. The present
approximation yields in finite dimensions an ideal glass transition similar to
that found in mean field. However, we find that along the RG flow the
properties associated with metastable glassy states, such as the
configurational entropy, are only defined up to a characteristic length scale
that diverges as one approaches the ideal glass transition. The critical
exponents characterizing the vicinity of the transition are the usual ones
associated with a first-order discontinuity fixed point. | cond-mat_dis-nn |
Particle size effects in the antiferromagnetic spinel CoRh$_2$O$_4$: We report the particle size dependent magnetic behaviour in the
antiferromagnetic spinel CoRh2O4. The nanoparticles were obtained by mechanical
milling of bulk material, prepared under sintering method. The XRD spectra show
that the samples are retaining the spinel structure. The particle size
decreases from 70 nm to 16 nm as the milling time increases from 12 hours to 60
hours. The magnetic measurements suggest that the antiferromagnetic ordering at
T$_N$ $\approx$ 27K exists in bulk as well as in nanoparticle samples. However,
the magnitude of the magnetization below T$_N$ increases with decreasing
particle size. | cond-mat_dis-nn |
Landau-Zener transition driven by a slow noise: The effect of a slow noise in non-diagonal matrix element, J(t), that
describes the diabatic level coupling, on the probability of the Landau-Zener
transition is studied. For slow noise, the correlation time, \tau_c, of J(t) is
much longer than the characteristic time of the transition. Existing theory for
this case suggests that the average transition probability is the result of
averaging of the conventional Landau-Zener probability, calculated for a given
constant J, over the distribution of J. We calculate a finite-\tau_c correction
to this classical result. Our main finding is that this correction is dominated
by sparse realizations of noise for which J(t) passes through zero within a
narrow time interval near the level crossing. Two models of noise, random
telegraph noise and gaussian noise, are considered. Naturally, in both models
the average probability of transition decreases upon decreasing \tau_c. For
gaussian noise we identify two domains of this fall-off with specific
dependencies of average transition probability on \tau_c. | cond-mat_dis-nn |
A New Method to Calculate the Spin-Glass Order Parameter of the
Two-Dimensional +/-J Ising Model: A new method to numerically calculate the $n$th moment of the spin overlap of
the two-dimensional $\pm J$ Ising model is developed using the identity derived
by one of the authors (HK) several years ago. By using the method, the $n$th
moment of the spin overlap can be calculated as a simple average of the $n$th
moment of the total spins with a modified bond probability distribution. The
values of the Binder parameter etc have been extensively calculated with the
linear size, $L$, up to L=23. The accuracy of the calculations in the present
method is similar to that in the conventional transfer matrix method with about
$10^{5}$ bond samples. The simple scaling plots of the Binder parameter and the
spin-glass susceptibility indicate the existence of a finite-temperature
spin-glass phase transition. We find, however, that the estimation of $T_{\rm
c}$ is strongly affected by the corrections to scaling within the present data
($L\leq 23$). Thus, there still remains the possibility that $T_{\rm c}=0$,
contrary to the recent results which suggest the existence of a
finite-temperature spin-glass phase transition. | cond-mat_dis-nn |
Replica Cluster Variational Method: the Replica Symmetric solution for
the 2D random bond Ising model: We present and solve the Replica Symmetric equations in the context of the
Replica Cluster Variational Method for the 2D random bond Ising model
(including the 2D Edwards-Anderson spin glass model). First we solve a
linearized version of these equations to obtain the phase diagrams of the model
on the square and triangular lattices. In both cases the spin-glass transition
temperatures and the tricritical point estimations improve largely over the
Bethe predictions. Moreover, we show that this phase diagram is consistent with
the behavior of inference algorithms on single instances of the problem.
Finally, we present a method to consistently find approximate solutions to the
equations in the glassy phase. The method is applied to the triangular lattice
down to T=0, also in the presence of an external field. | cond-mat_dis-nn |
The interpretation of broad diffuse maxima using superspace
crystallography: Single crystal diffuse scattering is generally interpreted using correlation
parameters that describe probabilities for certain configurations on a local
scale. In this paper we present a novel interpretation of diffuse maxima using
a disordered superspace approach. In (D+d)-dimensional superspace two
modulation functions are disordered along the superspace axis $\vec{a}_{s,i}$
for i = 1,..,D, while the periodicity along the internal dimensions is
maintained. This simple approach allows the generation of diffuse maxima of any
width at any position in reciprocal space. The extinction rules that are
introduced by superspace symmetry are also fulfilled by the diffuse maxima from
structures generated using the disordered superspace approach. In this
manuscript we demonstrate the disordered superspace approach using a simple a
simple two-dimensional binary disordered system. The extension of the approach
to (3+D)-dimensional superspace is trivial. The treatment of displacement and
magnetic disorder in a similar approach is straight forward. | cond-mat_dis-nn |
Exact Dynamical Equations for Kinetically-Constrained-Models: The mean-field theory of Kinetically-Constrained-Models is developed by
considering the Fredrickson-Andersen model on the Bethe lattice. Using certain
properties of the dynamics observed in actual numerical experiments we derive
asymptotic dynamical equations equal to those of Mode-Coupling-Theory.
Analytical predictions obtained for the dynamical exponents are successfully
compared with numerical simulations in a wide range of models including the
case of generic values of the connectivity and the facilitation, random pinning
and fluctuating facilitation. The theory is thus validated for both continuous
and discontinuous transition and also in the case of higher order critical
points characterized by logarithmic decays. | cond-mat_dis-nn |
Scaling the Temperature-dependent Boson Peak of Vitreous Silica with the
high-frequency Bulk Modulus derived from Brillouin Scattering Data: The position and strength of the boson peak in silica glass vary considerably
with temperature $T$. Such variations cannot be explained solely with changes
in the Debye energy. New Brillouin scattering measurements are presented which
allow determining the $T$-dependence of unrelaxed acoustic velocities. Using a
velocity based on the bulk modulus, scaling exponents are found which agree
with the soft-potential model. The unrelaxed bulk modulus thus appears to be a
good measure for the structural evolution of silica with $T$ and to set the
energy scale for the soft potentials. | cond-mat_dis-nn |
From Inherent Structures Deformation to Elastic Heterogeneities: Using a well defined soft model glass in the framework of Molecular Dynamics
simulations, the inherent structures are probed by means of a recently
developed deformation protocol that aims to capture the Dynamical
Heterogeneities (DH), as well as by the use of the isoconfigurational ensemble.
Comparisons of both methods are performed by extracting the corresponding
inherent characteristic length scales as the temperature of the system is
cooled down from the liquid to the glassy state. The obtained lengths grow and
depict an identical trend as the system falls out-off equilibrium, and appear
to converge to the characteristic length scale that characterizes the Elastic
Heterogeneities (EH) of the materials in the very low temperature limit, which
is deeply related to the properties of the glass. This provides a first
evidence of a relationship between DH and EH. | cond-mat_dis-nn |
Perturbative instability of non-ergodic phases in non-Abelian quantum
chains: An important challenge in the field of many-body quantum dynamics is to
identify non-ergodic states of matter beyond many-body localization (MBL).
Strongly disordered spin chains with non-Abelian symmetry and chains of
non-Abelian anyons are natural candidates, as they are incompatible with
standard MBL. In such chains, real space renormalization group methods predict
a partially localized, non-ergodic regime known as a quantum critical glass (a
critical variant of MBL). This regime features a tree-like hierarchy of
integrals of motion and symmetric eigenstates with entanglement entropy that
scales as a logarithmically enhanced area law. We argue that such tentative
non-ergodic states are perturbatively unstable using an analytic computation of
the scaling of off-diagonal matrix elements and accessible level spacing of
local perturbations. Our results indicate that strongly disordered chains with
non-Abelian symmetry display either spontaneous symmetry breaking or ergodic
thermal behavior at long times. We identify the relevant length and time scales
for thermalization: even if such chains eventually thermalize, they can exhibit
non-ergodic dynamics up to parametrically long time scales with a non-analytic
dependence on disorder strength. | cond-mat_dis-nn |
Scaling form of zero-field-cooled and field-cooled susceptibility in
superparamagnet: The scaling form of the normalized ZFC and FC susceptibility of
superparamagnets (SPM's) is presented as a function of the normalized
temperature $y$ ($=k_{B}T/K_{u}< V>$), normalized magnetic field $h$
($=H/H_{K}$), and the width $\sigma$ of the log-normal distribution of the
volumes of nanoparticles, based on the superparamagnetic blocking model with no
interaction between the nanoparticles. Here $<V>$ is the average volume,
$K_{u}$ is the anisotropy energy, and $H_{K}$ is the anisotropy field. Main
features of the experimental results reported in many SPM's can be well
explained in terms of the present model. The normalized FC susceptibility
increases monotonically increases as the normalized temperature $y$ decreases.
The normalized ZFC susceptibility exhibits a peak at the normalized blocking
temperature $y_{b}$ ($=k_{B}T_{b}/K_{u}< V>$), forming the $y_{b}$ vs $h$
diagram. For large $\sigma$ ($\sigma >0.4$), $y_{b}$ starts to increase with
increasing $h$, showing a peak at $h=h_{b}$, and decreases with further
increasing $h$. The maximum of $y_{b}$ at $h=h_{b}$ is due to the nonlinearity
of the Langevin function. For small $\sigma$, $y_{b}$ monotonically decreases
with increasing $h$. The derivative of the normalized FC magnetization with
respect to $h$ shows a peak at $h$ = 0 for small $y$. This is closely related
to the pinched form of $M_{FC}$ vs $H$ curve around $H$ = 0 observed in SPM's. | cond-mat_dis-nn |
Population spiking and bursting in next generation neural masses with
spike-frequency adaptation: Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking
into account the fatigue due to spike emissions and the consequent reduction of
the firing activity. We have studied the effect of this adaptation mechanism on
the macroscopic dynamics of excitatory and inhibitory networks of quadratic
integrate-and-fire (QIF) neurons coupled via exponentially decaying
post-synaptic potentials. In particular, we have studied the population
activities by employing an exact mean field reduction, which gives rise to next
generation neural mass models. This low-dimensional reduction allows for the
derivation of bifurcation diagrams and the identification of the possible
macroscopic regimes emerging both in a single and in two identically coupled
neural masses. In single populations SFA favours the emergence of population
bursts in excitatory networks, while it hinders tonic population spiking for
inhibitory ones. The symmetric coupling of two neural masses, in absence of
adaptation, leads to the emergence of macroscopic solutions with broken
symmetry: namely, chimera-like solutions in the inhibitory case and anti-phase
population spikes in the excitatory one. The addition of SFA leads to new
collective dynamical regimes exhibiting cross-frequency coupling (CFC) among
the fast synaptic time scale and the slow adaptation one, ranging from
anti-phase slow-fast nested oscillations to symmetric and asymmetric bursting
phenomena. The analysis of these CFC rhythms in the $\theta$-$\gamma$ range has
revealed that a reduction of SFA leads to an increase of the $\theta$ frequency
joined to a decrease of the $\gamma$ one. This is analogous to what reported
experimentally for the hippocampus and the olfactory cortex of rodents under
cholinergic modulation, that is known to reduce SFA. | cond-mat_dis-nn |
Algorithms for 3D rigidity analysis and a first order percolation
transition: A fast computer algorithm, the pebble game, has been used successfully to
study rigidity percolation on 2D elastic networks, as well as on a special
class of 3D networks, the bond-bending networks. Application of the pebble game
approach to general 3D networks has been hindered by the fact that the
underlying mathematical theory is, strictly speaking, invalid in this case. We
construct an approximate pebble game algorithm for general 3D networks, as well
as a slower but exact algorithm, the relaxation algorithm, that we use for
testing the new pebble game. Based on the results of these tests and additional
considerations, we argue that in the particular case of randomly diluted
central-force networks on BCC and FCC lattices, the pebble game is essentially
exact. Using the pebble game, we observe an extremely sharp jump in the largest
rigid cluster size in bond-diluted central-force networks in 3D, with the
percolating cluster appearing and taking up most of the network after a single
bond addition. This strongly suggests a first order rigidity percolation
transition, which is in contrast to the second order transitions found
previously for the 2D central-force and 3D bond-bending networks. While a first
order rigidity transition has been observed for Bethe lattices and networks
with ``chemical order'', this is the first time it has been seen for a regular
randomly diluted network. In the case of site dilution, the transition is also
first order for BCC, but results for FCC suggest a second order transition.
Even in bond-diluted lattices, while the transition appears massively first
order in the order parameter (the percolating cluster size), it is continuous
in the elastic moduli. This, and the apparent non-universality, make this phase
transition highly unusual. | cond-mat_dis-nn |
Spanning avalanches in the three-dimensional Gaussian Random Field Ising
Model with metastable dynamics: field dependence and geometrical properties: Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM)
with metastable dynamics at T=0 have been studied. Statistical analysis of the
field values for which avalanches occur has enabled a Finite-Size Scaling (FSS)
study of the avalanche density to be performed. Furthermore, direct measurement
of the geometrical properties of the avalanches has confirmed an earlier
hypothesis that several kinds of spanning avalanches with two different fractal
dimensions coexist at the critical point. We finally compare the phase diagram
of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at
T=0. | cond-mat_dis-nn |
1/f Noise in Electron Glasses: We show that 1/f noise is produced in a 3D electron glass by charge
fluctuations due to electrons hopping between isolated sites and a percolating
network at low temperatures. The low frequency noise spectrum goes as
\omega^{-\alpha} with \alpha slightly larger than 1. This result together with
the temperature dependence of \alpha and the noise amplitude are in good
agreement with the recent experiments. These results hold true both with a
flat, noninteracting density of states and with a density of states that
includes Coulomb interactions. In the latter case, the density of states has a
Coulomb gap that fills in with increasing temperature. For a large Coulomb gap
width, this density of states gives a dc conductivity with a hopping exponent
of approximately 0.75 which has been observed in recent experiments. For a
small Coulomb gap width, the hopping exponent approximately 0.5. | cond-mat_dis-nn |
Nonequilibrium localization and the interplay between disorder and
interactions: We study the nonequilibrium interplay between disorder and interactions in a
closed quantum system. We base our analysis on the notion of dynamical
state-space localization, calculated via the Loschmidt echo. Although
real-space and state-space localization are independent concepts in general, we
show that both perspectives may be directly connected through a specific choice
of initial states, namely, maximally localized states (ML-states). We show
numerically that in the noninteracting case the average echo is found to be
monotonically increasing with increasing disorder; these results are in
agreement with an analytical evaluation in the single particle case in which
the echo is found to be inversely proportional to the localization length. We
also show that for interacting systems, the length scale under which
equilibration may occur is upper bounded and such bound is smaller the greater
the average echo of ML-states. When disorder and interactions, both being
localization mechanisms, are simultaneously at play the echo features a
non-monotonic behaviour indicating a non-trivial interplay of the two
processes. This interplay induces delocalization of the dynamics which is
accompanied by delocalization in real-space. This non-monotonic behaviour is
also present in the effective integrability which we show by evaluating the gap
statistics. | cond-mat_dis-nn |
Vitrification of a monatomic 2D simple liquid: A monatomic simple liquid in two dimensions, where atoms interact
isotropically through the Lennard-Jones-Gauss potential [M. Engel and H.-R.
Trebin, Phys. Rev. Lett. 98, 225505 (2007)], is vitrified by the use of a rapid
cooling technique in a molecular dynamics simulation. Transformation to a
crystalline state is investigated at various temperatures and the
time-temperature-transformation (TTT) curve is determined. It is found that the
transformation time to a crystalline state is the shortest at a temerature 14%
below the melting temperature Tm and that at temperatures below Tv = 0.6 Tm the
transformation time is much longer than the available CPU time. This indicates
that a long-lived glassy state is realized for T < Tv. | cond-mat_dis-nn |
Hamiltonian equation of motion and depinning phase transition in
two-dimensional magnets: Based on the Hamiltonian equation of motion of the $\phi^4$ theory with
quenched disorder, we investigate the depinning phase transition of the
domain-wall motion in two-dimensional magnets. With the short-time dynamic
approach, we numerically determine the transition field, and the static and
dynamic critical exponents. The results show that the fundamental Hamiltonian
equation of motion belongs to a universality class very different from those
effective equations of motion. | cond-mat_dis-nn |
Phase Singularity Diffusion: We follow the trajectories of phase singularities at nulls of intensity in
the speckle pattern of waves transmitted through random media as the frequency
of the incident radiation is scanned in microwave experiments and numerical
simulations. Phase singularities are observed to diffuse with a linear increase
of the square displacement with frequency shift. The product of the diffusion
coefficient of phase singularities in the transmitted speckle pattern and the
photon diffusion coefficient through the random medium is proportional to the
square of the effective sample length. This provides the photon diffusion
coefficient and a method for characterizing the motion of dynamic material
systems. | cond-mat_dis-nn |
Thermal conductivity of molecular crystals with self-organizing disorder: The thermal conductivity of some orientational glasses of protonated C2H5OH
and deuterated C2D5OD ethanol, cyclic substances (cyclohexanol C6H11OH,
cyanocyclohexane C6H11CN, cyclohexene C6H10), and freon 112 (CFCl2)2 have been
analyzed in the temperature interval 2-130 K. The investigated substances
demonstrate new effects concerned with the physics of disordered systems.
Universal temperature dependences of the thermal conductivity of molecular
orientational glasses have been revealed. At low temperatures, the thermal
conductivity exhibits a universal behavior that can be described by the soft
potential model. At relatively high temperatures, the thermal conductivity has
a smeared maximum and than decreases with increase in the temperature, which
occurs typically in crystalline structures. | cond-mat_dis-nn |
Critical Networks Exhibit Maximal Information Diversity in
Structure-Dynamics Relationships: Network structure strongly constrains the range of dynamic behaviors
available to a complex system. These system dynamics can be classified based on
their response to perturbations over time into two distinct regimes, ordered or
chaotic, separated by a critical phase transition. Numerous studies have shown
that the most complex dynamics arise near the critical regime. Here we use an
information theoretic approach to study structure-dynamics relationships within
a unified framework and how that these relationships are most diverse in the
critical regime. | cond-mat_dis-nn |
The plasmon-polariton mirroring due to strong fluctuations of the
surface impedance: Scattering of TM-polarized surface plasmon-polariton waves (PPW) by a finite
segment of the metal-vacuum interface with randomly fluctuating surface
impedance is examined. Solution of the integral equation relating the scattered
field with the field of the incident PPW, valid for arbitrary scattering
intensity and arbitrary dissipative characteristics of the conductive medium,
is analyzed. As a measure of the PPW scattering, the Hilbert norm of the
integral scattering operator is used. The strength of the scattering is shown
to be determined not only by the parameters of the fluctuating impedance
(dispersion, correlation radius and the length of the inhomogeneity region) but
also by the conductivity of the metal. If the scattering operator norm is
small, the PPW is mainly scattered into the vacuum, thus losing its energy
through the excitation of quasi-isotropic bulk Norton-type waves above the
conducting surface. The intensity of the scattered field is expressed in terms
of the random impedance pair correlation function, whose dependence on the
incident and scattered wavenumbers shows that in the case of
random-impedance-induced scattering of PPW it is possible to observe the effect
analogous to Wood's anomalies of wave scattering on periodic gratings. Under
strong scattering, when the scattering operator norm becomes large compared to
unity, the radiation into free space is strongly suppressed, and, in the limit,
the incoming PPW is almost perfectly back-reflected from the inhomogeneous part
of the interface. This suggests that within the model of a dissipation-free
conducting medium, the surface polariton is unstable against arbitrary small
fluctuations of the medium polarizability. Transition from quasi-isotropic weak
scattering to nealy back-reflection under strong fluctuations of the impedance
is interpreted in terms of Anderson localization. | cond-mat_dis-nn |
Multifractal structure of Barkhausen noise: A signature of collective
dynamics at hysteresis loop: The field-driven magnetisation reversal processes in disordered systems
exhibit a collective behaviour that is manifested in the scale-invariance of
avalanches, closely related to underlying dynamical mechanisms. Using the
multifractal time series analysis, we study the structure of fluctuations at
different scales in the accompanying Barkhausen noise. The stochastic signal
represents the magnetisation discontinuities along the hysteresis loop of a
3-dimensional random field Ising model simulated for varied disorder strength
and driving rates. The analysis of the spectrum of the generalised Hurst
exponents reveals that the segments of the signal with large fluctuations
represent two distinct classes of stochastic processes in weak and strong
pinning regimes. Furthermore, increased driving rates have a profound effect on
the small fluctuation segments and broadening of the spectrum. The study of the
temporal correlations, sequences of avalanches, and their scaling features
complements the quantitative measures of the collective dynamics at the
hysteresis loop. The multifractal properties of Barkhausen noise describe the
dynamical state of domains and precisely discriminate the weak pinning,
permitting the motion of individual walls, from the mechanisms occurring in
strongly disordered systems. The multifractal nature of the reversal processes
is particularly relevant for currently investigated memory devices that utilize
a controlled motion of individual domain walls. | cond-mat_dis-nn |
Replacing neural networks by optimal analytical predictors for the
detection of phase transitions: Identifying phase transitions and classifying phases of matter is central to
understanding the properties and behavior of a broad range of material systems.
In recent years, machine-learning (ML) techniques have been successfully
applied to perform such tasks in a data-driven manner. However, the success of
this approach notwithstanding, we still lack a clear understanding of ML
methods for detecting phase transitions, particularly of those that utilize
neural networks (NNs). In this work, we derive analytical expressions for the
optimal output of three widely used NN-based methods for detecting phase
transitions. These optimal predictions correspond to the results obtained in
the limit of high model capacity. Therefore, in practice they can, for example,
be recovered using sufficiently large, well-trained NNs. The inner workings of
the considered methods are revealed through the explicit dependence of the
optimal output on the input data. By evaluating the analytical expressions, we
can identify phase transitions directly from experimentally accessible data
without training NNs, which makes this procedure favorable in terms of
computation time. Our theoretical results are supported by extensive numerical
simulations covering, e.g., topological, quantum, and many-body localization
phase transitions. We expect similar analyses to provide a deeper understanding
of other classification tasks in condensed matter physics. | cond-mat_dis-nn |
Universal spectral form factor for many-body localization: We theoretically study correlations present deep in the spectrum of
many-body-localized systems. An exact analytical expression for the spectral
form factor of Poisson spectra can be obtained and is shown to agree well with
numerical results on two models exhibiting many-body-localization: a disordered
quantum spin chain and a phenomenological $l$-bit model based on the existence
of local integrals of motion. We also identify a universal regime that is
insensitive to the global density of states as well as spectral edge effects. | cond-mat_dis-nn |
Chaos and residual correlations in pinned disordered systems: We study, using functional renormalization (FRG), two copies of an elastic
system pinned by mutually correlated random potentials. Short scale
decorrelation depend on a non trivial boundary layer regime with (possibly
multiple) chaos exponents. Large scale mutual displacement correlation behave
as $|x-x'|^{2 \zeta - \mu}$, the decorrelation exponent $\mu$ proportional to
the difference between Flory (or mean field) and exact roughness exponent
$\zeta$. For short range disorder $\mu >0$ but small, e.g. for random bond
interfaces $\mu = 5 \zeta - \epsilon$, $\epsilon=4-d$, and $\mu = \epsilon
(\frac{(2 \pi)^2}{36} - 1)$ for the one component Bragg glass. Random field
(i.e long range) disorder exhibits finite residual correlations (no chaos $\mu
= 0$) described by new FRG fixed points. Temperature and dynamic chaos
(depinning) are discussed. | cond-mat_dis-nn |
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