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Energy distribution of maxima and minima in a one-dimensional random
system: We study the energy distribution of maxima and minima of a simple
one-dimensional disordered Hamiltonian. We find that in systems with short
range correlated disorder there is energy separation between maxima and minima,
such that at fixed energy only one kind of stationary points is dominant in
number over the other. On the other hand, in the case of systems with long
range correlated disorder maxima and minima are completely mixed. | cond-mat_dis-nn |
Machine-learning assisted quantum control in random environment: Disorder in condensed matter and atomic physics is responsible for a great
variety of fascinating quantum phenomena, which are still challenging for
understanding, not to mention the relevant dynamical control. Here we introduce
proof of the concept and analyze neural network-based machine learning
algorithm for achieving feasible high-fidelity quantum control of a particle in
random environment. To explicitly demonstrate its capabilities, we show that
convolutional neural networks are able to solve this problem as they can
recognize the disorder and, by supervised learning, further produce the policy
for the efficient low-energy cost control of a quantum particle in a
time-dependent random potential. We have shown that the accuracy of the
proposed algorithm is enhanced by a higher-dimensional mapping of the disorder
pattern and using two neural networks, each properly trained for the given
task. The designed method, being computationally more efficient than the
gradient-descent optimization, can be applicable to identify and control
various noisy quantum systems on a heuristic basis. | cond-mat_dis-nn |
Spin relaxation in a Rashba semiconductor in an electric field: The impact of an external electric field on the spin relaxation in a
disordered two-dimensional electron system is studied within the framework of a
field-theoretical formulation. Generalized Bloch-equations for the diffusion
and the decay of an initial magnetization are obtained. The equations are
applied to the investigation of spin relaxation processes in an electric field. | cond-mat_dis-nn |
Analytical solutions for Ising models on high dimensional lattices: We use an m-vicinity method to examine Ising models on hypercube lattices of
high dimensions d>=3. This method is applicable for both short-range and
long-range interactions. We introduce a small parameter, which determines
whether the method can be used when calculating the free energy. When we
account for interaction with the nearest neighbors only, the value of this
parameter depends on the dimension of the lattice d. We obtain an expression
for the critical temperature in terms of the interaction constants that is in a
good agreement with results of computer simulations. For d=5, 6, 7, our
theoretical estimates match the experiments both qualitatively and
quantitatively. For d=3, 4, our method is sufficiently accurate for calculation
of the critical temperatures, however, it predicts a finite jump of the heat
capacity at the critical point. In the case of the three-dimensional lattice
(d=3), this contradicts to the commonly accepted ideas of the type of the
singularity at the critical point. For the four-dimensional lattice (d = 4) the
character of the singularity is under current discussion. For the dimensions
d=1, 2 the m-vicinity method is not applicable. | cond-mat_dis-nn |
A new view of the Lindemann criterion: The Lindemann criterion is reformulated in terms of the average shear modulus
$G_c$ of the melting crystal, indicating a critical melting shear strain which
is necessary to form the many different inherent states of the liquid. In glass
formers with covalent bonds, one has to distinguish between soft and hard
degrees of freedom to reach agreement. The temperature dependence of the
picosecond mean square displacements of liquid and crystal shows that there are
two separate contributions to the divergence of the viscosity with decreasing
temperature: the anharmonic increase of the shear modulus and a diverging
correlation length . | cond-mat_dis-nn |
Generalized Lyapunov Exponent and Transmission Statistics in
One-dimensional Gaussian Correlated Potentials: Distribution of the transmission coefficient T of a long system with a
correlated Gaussian disorder is studied analytically and numerically in terms
of the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect
of the disorder correlations on these quantities is considered in weak,
moderate and strong disorder for different models of correlation. Scaling
relations between the cumulants of lnT are obtained. The cumulants are treated
analytically within the semiclassical approximation in strong disorder, and
numerically for an arbitrary strength of the disorder. A small correlation
scale approximation is developed for calculation of the generalized LE in a
general correlated disorder. An essential effect of the disorder correlations
on the transmission statistics is found. In particular, obtained relations
between the cumulants and between them and the generalized LE show that, beyond
weak disorder, transmission fluctuations and deviation of their distribution
from the log-normal form (in a long but finite system) are greatly enhanced due
to the disorder correlations. Parametric dependence of these effects upon the
correlation scale is presented. | cond-mat_dis-nn |
Many-body localization in a fragmented Hilbert space: We study many-body localization (MBL) in a pair-hopping model exhibiting
strong fragmentation of the Hilbert space. We show that several Krylov
subspaces have both ergodic statistics in the thermodynamic limit and a
dimension that scales much slower than the full Hilbert space, but still
exponentially. Such a property allows us to study the MBL phase transition in
systems including more than $50$ spins. The different Krylov spaces that we
consider show clear signatures of a many-body localization transition, both in
the Kullback-Leibler divergence of the distribution of their level spacing
ratio and their entanglement properties. But they also present distinct
scalings with system size. Depending on the subspace, the critical disorder
strength can be nearly independent of the system size or conversely show an
approximately linear increase with the number of spins. | cond-mat_dis-nn |
New universal conductance fluctuation of mesoscopic systems in the
crossover regime from metal to insulator: We report a theoretical investigation on conductance fluctuation of
mesoscopic systems. Extensive numerical simulations on quasi-one dimensional,
two dimensional, and quantum dot systems with different symmetries (COE, CUE,
and CSE) indicate that the conductance fluctuation can reach a new universal
value in the crossover regime for systems with CUE and CSE symmetries. The
conductance fluctuation and higher order moments vs average conductance were
found to be universal functions from diffusive to localized regimes that depend
only on the dimensionality and symmetry. The numerical solution of DMPK
equation agrees with our result in quasi-one dimension. Our numerical results
in two dimensions suggest that this new universal conductance fluctuation is
related to the metal-insulator transition. | cond-mat_dis-nn |
Random maps and attractors in random Boolean networks: Despite their apparent simplicity, random Boolean networks display a rich
variety of dynamical behaviors. Much work has been focused on the properties
and abundance of attractors. The topologies of random Boolean networks with one
input per node can be seen as graphs of random maps. We introduce an approach
to investigating random maps and finding analytical results for attractors in
random Boolean networks with the corresponding topology. Approximating some
other non-chaotic networks to be of this class, we apply the analytic results
to them. For this approximation, we observe a strikingly good agreement on the
numbers of attractors of various lengths. We also investigate observables
related to the average number of attractors in relation to the typical number
of attractors. Here, we find strong differences that highlight the difficulties
in making direct comparisons between random Boolean networks and real systems.
Furthermore, we demonstrate the power of our approach by deriving some results
for random maps. These results include the distribution of the number of
components in random maps, along with asymptotic expansions for cumulants up to
the 4th order. | cond-mat_dis-nn |
Network Structure, Topology and Dynamics in Generalized Models of
Synchronization: We explore the interplay of network structure, topology, and dynamic
interactions between nodes using the paradigm of distributed synchronization in
a network of coupled oscillators. As the network evolves to a global steady
state, interconnected oscillators synchronize in stages, revealing network's
underlying community structure. Traditional models of synchronization assume
that interactions between nodes are mediated by a conservative process, such as
diffusion. However, social and biological processes are often non-conservative.
We propose a new model of synchronization in a network of oscillators coupled
via non-conservative processes. We study dynamics of synchronization of a
synthetic and real-world networks and show that different synchronization
models reveal different structures within the same network. | cond-mat_dis-nn |
Duality in finite-dimensional spin glasses: We present an analysis leading to a conjecture on the exact location of the
multicritical point in the phase diagram of spin glasses in finite dimensions.
The conjecture, in satisfactory agreement with a number of numerical results,
was previously derived using an ansatz emerging from duality and the replica
method. In the present paper we carefully examine the ansatz and reduce it to a
hypothesis on analyticity of a function appearing in the duality relation. Thus
the problem is now clearer than before from a mathematical point of view: The
ansatz, somewhat arbitrarily introduced previously, has now been shown to be
closely related to the analyticity of a well-defined function. | cond-mat_dis-nn |
Erratum: Small-world networks: Evidence for a crossover picture: We correct the value of the exponent \tau. | cond-mat_dis-nn |
Solvable Models of Supercooled Liquids in Three Dimensions: We introduce a supercooled liquid model and obtain parameter-free
quantitative predictions that are in excellent agreement with numerical
simulations, notably in the hard low-temperature region characterized by strong
deviations from Mode-Coupling-Theory behavior. The model is the
Fredrickson-Andersen Kinetically-Constrained-Model on the three-dimensional
$M$-layer lattice. The agreement has implications beyond the specific model
considered because the theory is potentially valid for many more systems,
including realistic models and actual supercooled liquids. | cond-mat_dis-nn |
On the ground states of the Bernasconi model: The ground states of the Bernasconi model are binary +1/-1 sequences of
length N with low autocorrelations. We introduce the notion of perfect
sequences, binary sequences with one-valued off-peak correlations of minimum
amount. If they exist, they are ground states. Using results from the
mathematical theory of cyclic difference sets, we specify all values of N for
which perfect sequences do exist and how to construct them. For other values of
N, we investigate almost perfect sequences, i.e. sequences with two-valued
off-peak correlations of minimum amount. Numerical and analytical results
support the conjecture that almost perfect sequences do exist for all values of
N, but that they are not always ground states. We present a construction for
low-energy configurations that works if N is the product of two odd primes. | cond-mat_dis-nn |
Hyperuniform vortex patterns at the surface of type-II superconductors: A many-particle system must posses long-range interactions in order to be
hyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical
simulations show, nevertheless, that a three-dimensional elastic-line array
with short-ranged repulsive interactions, such as vortex matter in a type-II
superconductor, forms at equilibrium a class-II hyperuniform two-dimensional
point pattern for any constant-$z$ cross section. In this case, density
fluctuations vanish isotropically as $\sim q^{\alpha}$ at small wave-vectors
$q$, with $\alpha=1$. This prediction includes the solid and liquid vortex
phases in the ideal clean case, and the liquid in presence of weak uncorrelated
disorder. We also show that the three-dimensional Bragg glass phase is
marginally hyperuniform, while the Bose glass and the liquid phase with
correlated disorder are expected to be non-hyperuniform at equilibrium.
Furthermore, we compare these predictions with experimental results on the
large-wavelength vortex density fluctuations of magnetically decorated vortex
structures nucleated in pristine, electron-irradiated and heavy-ion irradiated
superconducting BiSCCO samples in the mixed state. For most cases we find
hyperuniform two-dimensional point patterns at the superconductor surface with
an effective exponent $\alpha_{\text{eff}} \approx 1$. We interpret these
results in terms of a large-scale memory of the high-temperature line-liquid
phase retained in the glassy dynamics when field-cooling the vortex structures
into the solid phase. We also discuss the crossovers expected from the
dispersivity of the elastic constants at intermediate length-scales, and the
lack of hyperuniformity in the $x\,-y$ plane for lengths $q^{-1}$ larger than
the sample thickness due to finite-size effects in the $z$-direction. | cond-mat_dis-nn |
Relationship between non-exponentiality of relaxation and relaxation
time at the glass transition: By analyzing the experimental data for various glass-forming liquids and
polymers, we find that non-exponentiality $\beta$ and the relaxation time
$\tau$ are uniquely related: $\log(\tau)$ is an approximately linear function
of $1/\beta$, followed by a crossover to a higher linear slope. We rationalize
the observed relationship using a recently developed approach, in which the
problem of the glass transition is discussed as the elasticity problem. | cond-mat_dis-nn |
High values of disorder-generated multifractals and logarithmically
correlated processes: In the introductory section of the article we give a brief account of recent
insights into statistics of high and extreme values of disorder-generated
multifractals following a recent work by the first author with P. Le Doussal
and A. Rosso (FLR) employing a close relation between multifractality and
logarithmically correlated random fields. We then substantiate some aspects of
the FLR approach analytically for multifractal eigenvectors in the
Ruijsenaars-Schneider ensemble (RSE) of random matrices introduced by E.
Bogomolny and the second author by providing an ab initio calculation that
reveals hidden logarithmic correlations at the background of the
disorder-generated multifractality. In the rest we investigate numerically a
few representative models of that class, including the study of the highest
component of multifractal eigenvectors in the Ruijsenaars-Schneider ensemble. | cond-mat_dis-nn |
On Properties of Boundaries and Electron Conductivity in Mesoscopic
Polycrystalline Silicon Films for Memory Devices: We present the results of molecular dynamics modeling on the structural
properties of grain boundaries (GB) in thin polycrystalline films. The
transition from crystalline boundaries with low mismatch angle to amorphous
boundaries is investigated. It is shown that the structures of the GBs satisfy
a thermodynamical criterion. The potential energy of silicon atoms is closely
related with a geometrical quantity -- tetragonality of their coordination with
their nearest neighbors. A crossover of the length of localization is observed.
To analyze the crossover of the length of localization of the single-electron
states and properties of conductance of the thin polycrystalline film at low
temperature, we use a two-dimensional Anderson localization model, with the
random one-site electron charging energy for a single grain (dot), random
non-diagonal matrix elements, and random number of connections between the
neighboring grains. The results on the crossover behavior of localization
length of the single-electron states and characteristic properties of
conductance are presented in the region of parameters where the transition from
an insulator to a conductor regimes takes place. | cond-mat_dis-nn |
On the polyamorphism of fullerite-based orientational glasses: The dilatometric investigation in the temperature range of 2-28K shows that a
first-order polyamorphous transition occurs in the orientational glasses based
on C60 doped with H2, D2 and Xe. A polyamorphous transition was also detected
in C60 doped with Kr and He. It is observed that the hysteresis of thermal
expansion caused by the polyamorphous transition (and, hence, the transition
temperature) is essentially dependent on the type of doping gas. Both positive
and negative contributions to the thermal expansion were observed in the low
temperature phase of the glasses. The relaxation time of the negative
contribution occurs to be much longer than that of the positive contribution.
The positive contribution is found to be due to phonon and libron modes, whilst
the negative contribution is attributed to tunneling states of the C60
molecules. The characteristic time of the phase transformation from the low-T
phase to the high-T phase has been found for the C60-H2 system at 12K. A
theoretical model is proposed to interpret these observed phenomena. The
theoretical model proposed, includes a consideration of the nature of
polyamorphism in glasses, as well as the thermodynamics and kinetics of the
transition. A model of non-interacting tunneling states is used to explain the
negative contribution to the thermal expansion. The experimental data obtained
is considered within the framework of the theoretical model. From the
theoretical model the order of magnitude of the polyamorphous transition
temperature has been estimated. It is found that the late stage of the
polyamorphous transformation is described well by the Kolmogorov law with an
exponent of n=1. At this stage of the transformation, the two-dimensional phase
boundary moves along the normal, and the nucleation is not important. | cond-mat_dis-nn |
Cracks in random brittle solids: From fiber bundles to continuum
mechanics: Statistical models are essential to get a better understanding of the role of
disorder in brittle disordered solids. Fiber bundle models play a special role
as a paradigm, with a very good balance of simplicity and non-trivial effects.
We introduce here a variant of the fiber bundle model where the load is
transferred among the fibers through a very compliant membrane. This Soft
Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber
bundle model in 1D. Highlighting the continuum limit of the model allows to
compute an equivalent toughness for the fiber bundle and hence discuss
nucleation of a critical defect. The computation of the toughness allows for
drawing a simple connection with crack front propagation (depinning) models. | cond-mat_dis-nn |
Resonance width distribution for high-dimensional random media: We study the distribution of resonance widths P(G) for three-dimensional (3D)
random scattering media and analyze how it changes as a function of the
randomness strength. We are able to identify in P(G) the system-inherent
fingerprints of the metallic, localized, and critical regimes. Based on the
properties of resonance widths, we also suggest a new criterion for determining
and analyzing the metal-insulator transition. Our theoretical predictions are
verified numerically for the prototypical 3D tight-binding Anderson model. | cond-mat_dis-nn |
Activity patterns on random scale-free networks: Global dynamics arising
from local majority rules: Activity or spin patterns on random scale-free network are studied by mean
field analysis and computer simulations. These activity patterns evolve in time
according to local majority-rule dynamics which is implemented using (i)
parallel or synchronous updating and (ii) random sequential or asynchronous
updating. Our mean-field calculations predict that the relaxation processes of
disordered activity patterns become much more efficient as the scaling exponent
$\gamma$ of the scale-free degree distribution changes from $\gamma >5/2$ to
$\gamma < 5/2$. For $\gamma > 5/2$, the corresponding decay times increase as
$\ln(N)$ with increasing network size $N$ whereas they are independent of $N$
for $\gamma < 5/2$. In order to check these mean field predictions, extensive
simulations of the pattern dynamics have been performed using two different
ensembles of random scale-free networks: (A) multi-networks as generated by the
configuration method, which typically leads to many self-connections and
multiple edges, and (B) simple-networks without self-connections and multiple
edges. | cond-mat_dis-nn |
Non-Arrhenius Behavior of Secondary Relaxation in Supercooled Liquids: Dielectric relaxation spectroscopy (1 Hz - 20 GHz) has been performed on
supercooled glass-formers from the temperature of glass transition (T_g) up to
that of melting. Precise measurements particularly in the frequencies of
MHz-order have revealed that the temperature dependences of secondary
beta-relaxation times deviate from the Arrhenius relation in well above T_g.
Consequently, our results indicate that the beta-process merges into the
primary alpha-mode around the melting temperature, and not at the dynamical
transition point T which is approximately equal to 1.2 T_g. | cond-mat_dis-nn |
Bond dilution in the 3D Ising model: a Monte Carlo study: We study by Monte Carlo simulations the influence of bond dilution on the
three-dimensional Ising model. This paradigmatic model in its pure version
displays a second-order phase transition with a positive specific heat critical
exponent $\alpha$. According to the Harris criterion disorder should hence lead
to a new fixed point characterized by new critical exponents. We have
determined the phase diagram of the diluted model, between the pure model limit
and the percolation threshold. For the estimation of critical exponents, we
have first performed a finite-size scaling study, where we concentrated on
three different dilutions. We emphasize in this work the great influence of the
cross-over phenomena between the pure, disorder and percolation fixed points
which lead to effective critical exponents dependent on the concentration. In a
second set of simulations, the temperature behaviour of physical quantities has
been studied in order to characterize the disorder fixed point more accurately.
In particular this allowed us to estimate ratios of some critical amplitudes.
In accord with previous observations for other models this provides stronger
evidence for the existence of the disorder fixed point since the amplitude
ratios are more sensitive to the universality class than the critical
exponents. Moreover, the question of non-self-averaging at the disorder fixed
point is investigated and compared with recent results for the bond-diluted
$q=4$ Potts model. Overall our numerical results provide evidence that, as
expected on theoretical grounds, the critical behaviour of the bond-diluted
model is governed by the same universality class as the site-diluted model. | cond-mat_dis-nn |
Analytical representations for relaxation functions of glasses: Analytical representations in the time and frequency domains are derived for
the most frequently used phenomenological fit functions for non-Debye
relaxation processes. In the time domain the relaxation functions corresponding
to the complex frequency dependent Cole-Cole, Cole-Davidson and
Havriliak-Negami susceptibilities are also represented in terms of
$H$-functions. In the frequency domain the complex frequency dependent
susceptibility function corresponding to the time dependent stretched
exponential relaxation function is given in terms of $H$-functions. The new
representations are useful for fitting to experiment. | cond-mat_dis-nn |
Crossover from Scale-Free to Spatial Networks: In many networks such as transportation or communication networks, distance
is certainly a relevant parameter. In addition, real-world examples suggest
that when long-range links are existing, they usually connect to hubs-the well
connected nodes. We analyze a simple model which combine both these
ingredients--preferential attachment and distance selection characterized by a
typical finite `interaction range'. We study the crossover from the scale-free
to the `spatial' network as the interaction range decreases and we propose
scaling forms for different quantities describing the network. In particular,
when the distance effect is important (i) the connectivity distribution has a
cut-off depending on the node density, (ii) the clustering coefficient is very
high, and (iii) we observe a positive maximum in the degree correlation
(assortativity) which numerical value is in agreement with empirical
measurements. Finally, we show that if the number of nodes is fixed, the
optimal network which minimizes both the total length and the diameter lies in
between the scale-free and spatial networks. This phenomenon could play an
important role in the formation of networks and could be an explanation for the
high clustering and the positive assortativity which are non trivial features
observed in many real-world examples. | cond-mat_dis-nn |
Managing catastrophic changes in a collective: We address the important practical issue of understanding, predicting and
eventually controlling catastrophic endogenous changes in a collective. Such
large internal changes arise as macroscopic manifestations of the microscopic
dynamics, and their presence can be regarded as one of the defining features of
an evolving complex system. We consider the specific case of a multi-agent
system related to the El Farol bar model, and show explicitly how the
information concerning such large macroscopic changes becomes encoded in the
microscopic dynamics. Our findings suggest that these large endogenous changes
can be avoided either by pre-design of the collective machinery itself, or in
the post-design stage via continual monitoring and occasional `vaccinations'. | cond-mat_dis-nn |
Statistical Mechanics of Online Learning of Drifting Concepts : A
Variational Approach: We review the application of Statistical Mechanics methods to the study of
online learning of a drifting concept in the limit of large systems. The model
where a feed-forward network learns from examples generated by a time dependent
teacher of the same architecture is analyzed. The best possible generalization
ability is determined exactly, through the use of a variational method. The
constructive variational method also suggests a learning algorithm. It depends,
however, on some unavailable quantities, such as the present performance of the
student. The construction of estimators for these quantities permits the
implementation of a very effective, highly adaptive algorithm. Several other
algorithms are also studied for comparison with the optimal bound and the
adaptive algorithm, for different types of time evolution of the rule. | cond-mat_dis-nn |
Disorder driven itinerant quantum criticality of three dimensional
massless Dirac fermions: Progress in the understanding of quantum critical properties of itinerant
electrons has been hindered by the lack of effective models which are amenable
to controlled analytical and numerically exact calculations. Here we establish
that the disorder driven semimetal to metal quantum phase transition of three
dimensional massless Dirac fermions could serve as a paradigmatic toy model for
studying itinerant quantum criticality, which is solved in this work by exact
numerical and approximate field theoretic calculations. As a result, we
establish the robust existence of a non-Gaussian universality class, and also
construct the relevant low energy effective field theory that could guide the
understanding of quantum critical scaling for many strange metals. Using the
kernel polynomial method (KPM), we provide numerical results for the calculated
dynamical exponent ($z$) and correlation length exponent ($\nu$) for the
disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition
at the Dirac point for several types of disorder, establishing its universal
nature and obtaining the numerical scaling functions in agreement with our
field theoretical analysis. | cond-mat_dis-nn |
Distribution of zeros of the S-matrix of chaotic cavities with localized
losses and Coherent Perfect Absorption: non-perturbative results: We employ the Random Matrix Theory framework to calculate the density of
zeroes of an $M$-channel scattering matrix describing a chaotic cavity with a
single localized absorber embedded in it. Our approach extends beyond the
weak-coupling limit of the cavity with the channels and applies for any
absorption strength. Importantly it provides an insight for the optimal amount
of loss needed to realize a chaotic coherent perfect absorbing (CPA) trap. Our
predictions are tested against simulations for two types of traps: a complex
network of resonators and quantum graphs. | cond-mat_dis-nn |
Intermittent dynamics and logarithmic domain growth during the spinodal
decomposition of a glass-forming liquid: We use large-scale molecular dynamics simulations of a simple glass-forming
system to investigate how its liquid-gas phase separation kinetics depends on
temperature. A shallow quench leads to a fully demixed liquid-gas system
whereas a deep quench makes the dense phase undergo a glass transition and
become an amorphous solid. This glass has a gel-like bicontinuous structure
that evolves very slowly with time and becomes fully arrested in the limit
where thermal fluctuations become negligible. We show that the phase separation
kinetics changes qualitatively with temperature, the microscopic dynamics
evolving from a surface tension-driven diffusive motion at high temperature to
a strongly intermittent, heterogeneous and thermally activated dynamics at low
temperature, with a logarithmically slow growth of the typical domain size.
These results shed light on recent experimental observations of various porous
materials produced by arrested spinodal decomposition, such as nonequilibrium
colloidal gels and bicontinuous polymeric structures, and they elucidate the
microscopic mechanisms underlying a specific class of viscoelastic phase
separation. | cond-mat_dis-nn |
The Cavity Approach to Noisy Learning in Nonlinear Perceptrons: We analyze the learning of noisy teacher-generated examples by nonlinear and
differentiable student perceptrons using the cavity method. The generic
activation of an example is a function of the cavity activation of the example,
which is its activation in the perceptron that learns without the example. Mean
field equations for the macroscopic parameters and the stability condition
yield results consistent with the replica method. When a single value of the
cavity activation maps to multiple values of the generic activation, there is a
competition in learning strategy between preferentially learning an example and
sacrificing it in favor of the background adjustment. We find parameter regimes
in which examples are learned preferentially or sacrificially, leading to a gap
in the activation distribution. Full phase diagrams of this complex system are
presented, and the theory predicts the existence of a phase transition from
poor to good generalization states in the system. Simulation results confirm
the theoretical predictions. | cond-mat_dis-nn |
Machine learning assisted measurement of local topological invariants: The continuous effort towards topological quantum devices calls for an
efficient and non-invasive method to assess the conformity of components in
different topological phases. Here, we show that machine learning paves the way
towards non-invasive topological quality control. To do so, we use a local
topological marker, able to discriminate between topological phases of
one-dimensional wires. The direct observation of this marker in solid state
systems is challenging, but we show that an artificial neural network can learn
to approximate it from the experimentally accessible local density of states.
Our method distinguishes different non-trivial phases, even for systems where
direct transport measurements are not available and for composite systems. This
new approach could find significant use in experiments, ranging from the study
of novel topological materials to high-throughput automated material design. | cond-mat_dis-nn |
Structural Signatures for Thermodynamic Stability in Vitreous Silica:
Insight from Machine Learning and Molecular Dynamics Simulations: The structure-thermodynamic stability relationship in vitreous silica is
investigated using machine learning and a library of 24,157 inherent structures
generated from melt-quenching and replica exchange molecular dynamics
simulations. We find the thermodynamic stability, i.e., enthalpy of the
inherent structure ($e_{\mathrm{IS}}$), can be accurately predicted by both
linear and nonlinear machine learning models from numeric structural
descriptors commonly used to characterize disordered structures. We find
short-range features become less indicative of thermodynamic stability below
the fragile-to-strong transition. On the other hand, medium-range features,
especially those between 2.8-~6 $\unicode{x212B}$;, show consistent
correlations with $e_{\mathrm{IS}}$ across the liquid and glass regions, and
are found to be the most critical to stability prediction among features from
different length scales. Based on the machine learning models, a set of five
structural features that are the most predictive of the silica glass stability
is identified. | cond-mat_dis-nn |
Origin of the unusual dependence of Raman D band on excitation
wavelength in graphite-like materials: We have revisited the still unresolved puzzle of the dispersion of the Raman
disordered-induced D band as a function of laser excitation photon energy E$_L$
in graphite-like materials. We propose that the D-mode is a combination of an
optic phonon at the K-point in the Brillioun zone and an acoustic phonon whose
momentum is determined uniquely by the double resonance condition. The fit of
the experimental data with the double-resonance model yields the reduced
effective mass of 0.025m$_{e}$ for the electron-hole pairs corresponding to the
A$_{2}$ transition, in agreement with other experiments. The model can also
explain the difference between $\omega_S$ and $\omega_{AS}$ for D and
D$^{\star}$ modes, and predicts its dependence on the Raman excitation
frequency. | cond-mat_dis-nn |
Infrared-Induced Sluggish Dynamics in the GeSbTe Electron Glass: The electron-glass dynamics of Anderson-localized GeSbTe films is
dramatically slowed-down following a brief infrared illumination that increases
the system carrier-concentration (and thus its conductance). These results
demonstrate that the dynamics exhibited by electron-glasses is more sensitive
to carrier-concentration than to disorder. In turn, this seems to imply that
many-body effects such as the Orthogonality Catastrophe must play a role in the
sluggish dynamics observed in the intrinsic electron-glasses. | cond-mat_dis-nn |
Inducing periodicity in lattices of chaotic maps with advection: We investigate a lattice of coupled logistic maps where, in addition to the
usual diffusive coupling, an advection term parameterized by an asymmetry in
the coupling is introduced. The advection term induces periodic behavior on a
significant number of non-periodic solutions of the purely diffusive case. Our
results are based on the characteristic exponents for such systems, namely the
mean Lyapunov exponent and the co-moving Lyapunov exponent. In addition, we
study how to deal with more complex phenomena in which the advective velocity
may vary from site to site. In particular, we observe wave-like pulses to
appear and disappear intermittently whenever the advection is spatially
inhomogeneous. | cond-mat_dis-nn |
Statistical Mechanics of Dictionary Learning: Finding a basis matrix (dictionary) by which objective signals are
represented sparsely is of major relevance in various scientific and
technological fields. We consider a problem to learn a dictionary from a set of
training signals. We employ techniques of statistical mechanics of disordered
systems to evaluate the size of the training set necessary to typically succeed
in the dictionary learning. The results indicate that the necessary size is
much smaller than previously estimated, which theoretically supports and/or
encourages the use of dictionary learning in practical situations. | cond-mat_dis-nn |
Anomalously Strong Nonlinearity of Unswept Quartz Acoustic Cavities at
Liquid Helium Temperatures: We demonstrate a variety of nonlinear phenomena at extremely low powers in
cryogenic acoustic cavities fabricated from quartz material, which have not
undergone any electrodiffusion processes. Nonlinear phenomena observed include
lineshape discontinuities, power response discontinuities, quadrature
oscillations and self-induced transparency. These phenomena are attributed to
nonlinear dissipation through a large number of randomly distributed heavy
trapped ions, which would normally be removed by electrodiffusion. A simple
mean-field model predicts most of the observed phenomena. In contrast to
Duffing-like systems, this system shows an unusual mechanism of nonlinearity,
which is not related to crystal anharmonisity. | cond-mat_dis-nn |
Avalanches in Tip-Driven Interfaces in Random Media: We analyse by numerical simulations and scaling arguments the avalanche
statistics of 1-dimensional elastic interfaces in random media driven at a
single point. Both global and local avalanche sizes are power-law distributed,
with universal exponents given by the depinning roughness exponent $\zeta$ and
the interface dimension $d$, and distinct from their values in the uniformly
driven case. A crossover appears between uniformly driven behaviour for small
avalanches, and point driven behaviour for large avalanches. The scale of the
crossover is controlled by the ratio between the stiffness of the pulling
spring and the elasticity of the interface; it is visible both in the global
and local avalanche-size distributions, as in the average spatial avalanche
shape. Our results are relevant to model experiments involving locally driven
elastic manifolds at low temperatures, such as magnetic domain walls or vortex
lines in superconductors. | cond-mat_dis-nn |
The Leontovich boundary conditions and calculation of effective
impedance of inhomogeneous metal: We bring forward rather simple algorithm allowing us to calculate the
effective impedance of inhomogeneous metals in the frequency region where the
local Leontovich (the impedance) boundary conditions are justified. The
inhomogeneity is due to the properties of the metal or/and the surface
roughness. Our results are nonperturbative ones with respect to the
inhomogeneity amplitude. They are based on the recently obtained exact result
for the effective impedance of inhomogeneous metals with flat surfaces.
One-dimension surfaces inhomogeneities are examined. Particular attention is
paid to the influence of generated evanescent waves on the reflection
characteristics. We show that if the surface roughness is rather strong, the
element of the effective impedance tensor relating to the p- polarization state
is much greater than the input local impedance. As examples, we calculate: i)
the effective impedance for a flat surface with strongly nonhomogeneous
periodic strip-like local impedance; ii) the effective impedance associated
with one-dimensional lamellar grating. For the problem (i) we also present
equations for the forth lines of the Pointing vector in the vicinity of the
surface. | cond-mat_dis-nn |
StrainTensorNet: Predicting crystal structure elastic properties using
SE(3)-equivariant graph neural networks: Accurately predicting the elastic properties of crystalline solids is vital
for computational materials science. However, traditional atomistic scale ab
initio approaches are computationally intensive, especially for studying
complex materials with a large number of atoms in a unit cell. We introduce a
novel data-driven approach to efficiently predict the elastic properties of
crystal structures using SE(3)-equivariant graph neural networks (GNNs). This
approach yields important scalar elastic moduli with the accuracy comparable to
recent data-driven studies. Importantly, our symmetry-aware GNNs model also
enables the prediction of the strain energy density (SED) and the associated
elastic constants, the fundamental tensorial quantities that are significantly
influenced by a material's crystallographic group. The model consistently
distinguishes independent elements of SED tensors, in accordance with the
symmetry of the crystal structures. Finally, our deep learning model possesses
meaningful latent features, offering an interpretable prediction of the elastic
properties. | cond-mat_dis-nn |
Monte Carlo studies of the chiral and spin orderings of the
three-dimensional Heisenberg spin glass: The nature of the ordering of the three-dimensional isotropic Heisenberg spin
glass with nearest-neighbor random Gaussian coupling is studied by extensive
Monte Carlo simulations. Several independent physical quantities are measured
both for the spin and for the chirality, including the correlation-length
ratio, the Binder ratio, the glass order parameter, the overlap distribution
function and the non-self-averageness parameter. By controlling the effect of
the correction-to-scaling, we have obtained a numerical evidence for the
occurrence of successive chiral-glass and spin-glass transitions at nonzero
temperatures, T_{CG} > T_{SG} > 0. Hence, the spin and the chirality are
decoupled in the ordering of the model. The chiral-glass exponents are
estimated to be \nu_{CG}=1.4+-0.2 and \eta_{CG}=0.6+-0.2, indicating that the
chiral-glass transition lies in a universality class different from that of the
Ising spin glass. The possibility that the spin and chiral sectors undergo a
simultaneous Kosterlitz-Thouless-type transition is ruled out. The chiral-glass
state turns out to be non-self-averaging, possibly accompanying a one-step-like
peculiar replica-symmetry breaking. Implications to the chirality scenario of
experimental spin-glass transitions are discussed. | cond-mat_dis-nn |
Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D
$\pm J$ Random-Bond Ising Model: The statistics of the ground-state and domain-wall energies for the
two-dimensional random-bond Ising model on square lattices with independent,
identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of
$J_{ij}= +1$ are studied. We are able to consider large samples of up to
$320^2$ spins by using sophisticated matching algorithms. We study $L \times L$
systems, but we also consider $L \times M$ samples, for different aspect ratios
$R = L / M$. We find that the scaling behavior of the ground-state energy and
its sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le
1 - p_c$) are characterized by simple scaling functions. In particular, the
fluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass
region the average domain-wall energy converges to a finite nonzero value as
the sample size becomes infinite, holding $R$ fixed. Here, large finite-size
effects are visible, which can be explained for all $p$ by a single exponent
$\omega\approx 2/3$, provided higher-order corrections to scaling are included.
Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: the
distribution of the domain-wall energies converges to a Gaussian for $R \to 0$,
although the domain walls of neighboring subsystems of size $L \times L$ are
not independent. | cond-mat_dis-nn |
Phase diagram of disordered fermion model on two-dimensional square
lattice with $π$-flux: A fermion model with random on-site potential defined on a two-dimensional
square lattice with $\pi$-flux is studied. The continuum limit of the model
near the zero energy yields Dirac fermions with random potentials specified by
four independent coupling constants. The basic symmetry of the model is
time-reversal invariance. Moreover, it turns out that the model has enhanced
(chiral) symmetry on several surfaces in the four-dimensional space of the
coupling constants. It is shown that one of the surfaces with chiral symmetry
has Sp(n)$\times$Sp(n) symmety whereas others have U(2n) symmetry, both of
which are broken to Sp(n), and the fluctuation around a saddle point is
described, respectively, by Sp($n)_2$ WZW model and U(2n)/Sp(n) nonlinear sigma
model. Based on these results, we propose a phase diagram of the model. | cond-mat_dis-nn |
Boundary-driven Lindblad dynamics of random quantum spin chains : strong
disorder approach for the relaxation, the steady state and the current: The Lindblad dynamics of the XX quantum chain with large random fields $h_j$
(the couplings $J_j$ can be either uniform or random) is considered for
boundary-magnetization-drivings acting on the two end-spins. Since each
boundary-reservoir tends to impose its own magnetization, we first study the
relaxation spectrum in the presence of a single reservoir as a function of the
system size via some boundary-strong-disorder renormalization approach. The
non-equilibrium-steady-state in the presence of two reservoirs can be then
analyzed from the effective renormalized Linbladians associated to the two
reservoirs. The magnetization is found to follow a step profile, as found
previously in other localized chains. The strong disorder approach allows to
compute explicitly the location of the step of the magnetization profile and
the corresponding magnetization-current for each disordered sample in terms of
the random fields and couplings. | cond-mat_dis-nn |
Comment on "Scaling behavior of classical wave transport in mesoscopic
media at the localization transition": We emphasize the importance of the position dependence of the diffusion
coefficient D(r) in the self-consistent theory of localization and argue that
the scaling law T ~ ln(L)/L^2 obtained by Cheung and Zhang [Phys. Rev. B 72,
235102 (2005)] for the average transmission coefficient T of a disordered slab
of thickness L at the localization transition is an artifact of replacing D(r)
by its harmonic mean. The correct scaling T ~ 1/L^2 is obtained by properly
treating the position dependence of D(r). | cond-mat_dis-nn |
Many-Body-Localization Transition : strong multifractality spectrum for
matrix elements of local operators: For short-ranged disordered quantum models in one dimension, the
Many-Body-Localization is analyzed via the adaptation to the Many-Body context
[M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless
point of view on the Anderson transition : the question is whether a local
interaction between two long chains is able to reshuffle completely the
eigenstates (Delocalized phase with a volume-law entanglement) or whether the
hybridization between tensor states remains limited (Many-Body-Localized Phase
with an area-law entanglement). The central object is thus the level of
Hybridization induced by the matrix elements of local operators, as compared
with the difference of diagonal energies. The multifractal analysis of these
matrix elements of local operators is used to analyze the corresponding
statistics of resonances. Our main conclusion is that the critical point is
characterized by the Strong-Multifractality Spectrum $f(0 \leq \alpha \leq
2)=\frac{\alpha}{2}$, well known in the context of Anderson Localization in
spaces of effective infinite dimensionality, where the size of the Hilbert
space grows exponentially with the volume. Finally, the possibility of a
delocalized non-ergodic phase near criticality is discussed. | cond-mat_dis-nn |
Laser beam filamentation in fractal aggregates: We investigate filamentation of a cw laser beam in soft matter such as
colloidal suspensions and fractal gels. The process, driven by
electrostriction, is strongly affected by material properties, which are taken
into account via the static structure factor, and have impact on the statistics
of the light filaments. | cond-mat_dis-nn |
Laser beam filamentation in fractal aggregates: We investigate filamentation of a cw laser beam in soft matter such as
colloidal suspensions and fractal gels. The process, driven by
electrostriction, is strongly affected by material properties, which are taken
into account via the static structure factor, and have impact on the statistics
of the light filaments. | cond-mat_dis-nn |
Capillary forces in the acoustics of patchy-saturated porous media: A linearized theory of the acoustics of porous elastic formations, such as
rocks, saturated with two different viscous fluids is generalized to take into
account a pressure discontinuity across the fluid boundaries. The latter can
arise due to the surface tension of the membrane separating the fluids. We show
that the frequency-dependent bulk modulus $\tilde{K}(\omega)$ for wave lengths
longer than the characteristic structural dimensions of the fluid patches has a
similar analytic behavior as in the case of a vanishing membrane stiffness and
depends on the same parameters of the fluid-distribution topology. The effect
of the capillary stiffness can be accounted by renormalizing the coefficients
of the leading terms in the low-frequency asymptotic of $\tilde{K}(\omega)$. | cond-mat_dis-nn |
Extremal statistics of entanglement eigenvalues can track the many-body
localized to ergodic transition: Some interacting disordered many-body systems are unable to thermalize when
the quenched disorder becomes larger than a threshold value. Although several
properties of nonzero energy density eigenstates (in the middle of the
many-body spectrum) exhibit a qualitative change across this many-body
localization (MBL) transition, many of the commonly-used diagnostics only do so
over a broad transition regime. Here, we provide evidence that the transition
can be located precisely even at modest system sizes by sharply-defined changes
in the distribution of extremal eigenvalues of the reduced density matrix of
subsystems. In particular, our results suggest that $p* = \lim_{\lambda_2
\rightarrow \ln(2)^{+}}P_2(\lambda_2)$, where $P_2(\lambda_2)$ is the
probability distribution of the second lowest entanglement eigenvalue
$\lambda_2$, behaves as an ''order-parameter'' for the MBL phase: $p*> 0$ in
the MBL phase, while $p* = 0$ in the ergodic phase with thermalization. Thus,
in the MBL phase, there is a nonzero probability that a subsystem is entangled
with the rest of the system only via the entanglement of one subsystem qubit
with degrees of freedom outside the region. In contrast, this probability
vanishes in the thermal phase. | cond-mat_dis-nn |
Information on mean, fluctuation and synchrony conveyed by a population
of firing neurons: A population of firing neurons is expected to carry not only mean firing rate
but also its fluctuation and synchrony among neurons. In order to examine this
possibility, we have studied responses of neuronal ensembles to three kinds of
inputs: mean-, fluctuation- and synchrony-driven inputs. The generalized
rate-code model including additive and multiplicative noise (H. Hasegawa, Phys.
Rev. E {\bf 75}, 051904 (2007)) has been studied by direct simulations (DSs)
and the augmented moment method (AMM) in which equations of motion for mean
firing rate, fluctuation and synchrony are derived. Results calculated by the
AMM are in good agreement with those by DSs. The independent component analysis
(ICA) of our results has shown that mean firing rate, fluctuation (or
variability) and synchrony may carry independent information in the population
rate-code model. The input-output relation of mean firing rates is shown to
have higher sensitivity for larger multiplicative noise, as recently observed
in prefrontal cortex. A comparison is made between results obtained by the
integrate-and-fire (IF) model and our rate-code model. The relevance of our
results to experimentally obtained data is also discussed. | cond-mat_dis-nn |
Phase diagram of superfluid 3He in "nematically ordered" aerogel: Results of experiments with liquid 3He immersed in a new type of aerogel are
described. This aerogel consists of Al2O3 strands which are nearly parallel to
each other, so we call it as a "nematically ordered" aerogel. At all used
pressures a superfluid transition was observed and a superfluid phase diagram
was measured. Possible structures of the observed superfluid phases are
discussed. | cond-mat_dis-nn |
Two-dimensional systems of elongated particles: From diluted to dense: This chapter is devoted to the analysis of jamming and percolation behavior
of two-dimensional systems of elongated particles. We consider both continuous
and discrete spaces (with the special attention to the square lattice), as well
the systems with isotropically deposited and aligned particles. Overviews of
different analytical and computational methods and main results are presented. | cond-mat_dis-nn |
Self-consistent study of Anderson localization in the Anderson-Hubbard
model in two and three dimensions: We consider the change in electron localization due to the presence of
electron-electron repulsion in the \HA model. Taking into account local
Mott-Hubbard physics and static screening of the disorder potential, the system
is mapped onto an effective single-particle Anderson model, which is studied
within the self-consistent theory of electron localization. We find rich
nonmonotonic behavior of the localization length $\xi$ in two-dimensional
systems, including an interaction-induced exponential enhancement of $\xi$ for
small and intermediate disorders although $\xi$ remains finite. In three
dimensions we identify for half filling a Mott-Hubbard-assisted Anderson
localized phase existing between the metallic and the Mott-Hubbard-gapped
phases. For small $U$ there is re-entrant behavior from the Anderson localized
phase to the metallic phase. | cond-mat_dis-nn |
Monte Carlo Simulations of a Generalized n--spin facilitated kinetic
Ising Model: A kinetic Ising model is analyzed where spin variables correspond to lattice
cells with mobile or immobile particles. Introducing additional restrictions
for the flip processes according to the n-spin facilitated kinetic Ising model
and using Monte Carlo methods we study the freezing process under the influence
of an additional nearest-neighbor interaction. The stretched exponential decay
of the auto-correlation function is observed and the exponent $\gamma$ as well
as the relaxation time are determined depending on the activation energy $h$
and the short range coupling $J$. The magnetization corresponding to the
density of immobile particles is found to be the controlling parameter for the
dynamic evolution. | cond-mat_dis-nn |
Can Local Stress Enhancement Induce Stability in Fracture Processes?
Part II: The Shielding Effect: We use the local load sharing fiber bundle model to demonstrate a shielding
effect where strong fibers protect weaker ones. This effect exists due to the
local stress enhancement around broken fibers in the local load sharing model,
and it is therefore not present in the equal load sharing model. The shielding
effect is prominent only after the initial disorder-driven part of the fracture
process has finished, and if the fiber bundle has not reached catastrophic
failure by this point, then the shielding increases the critical damage of the
system, compared to equal load sharing. In this sense, the local stress
enhancement may make the fracture process more stable, but at the cost of
reduced critical force. | cond-mat_dis-nn |
Eight orders of dynamical clusters and hard-spheres in the glass
transition: The nature may be disclosed that the glass transition is only determined by
the intrinsic 8 orders of instant 2-D mosaic geometric structures, without any
presupposition and relevant parameter. An interface excited state on the
geometric structures comes from the additional Lindemann distance increment,
which is a vector with 8 orders of relaxation times, 8 orders of additional
restoring force moment (ARFM), quantized energy and extra volume. Each order of
anharmonic ARFM gives rise to an additional position-asymmetry on a 2-D
projection plane of a reference particle, thus, in removing additional
position-asymmetry, the 8 orders of 2-D clusters and hard-spheres accompanied
with the 4 excited interface relaxations of the reference particle have been
illustrated. Dynamical behavior comes of the slow inverse energy cascade to
generate 8 orders of clusters, to thaw a solid-domain, and the fast cascade to
relax tension and rearrange structure. This model provides a unified mechanism
to interpret hard-sphere, compacting cluster, free volume, cage, jamming
behaviors, geometrical frustration, reptation, Ising model, breaking solid
lattice, percolation, cooperative migration and orientation, critical
entanglement chain length and structure rearrangements. It also directly
deduces a series of quantitative values for the average energy of cooperative
migration in one direction, localized energy independent of temperature and the
activation energy to break solid lattice. In a flexible polymer system, there
are all 320 different interface excited states that have the same quantized
excited energy but different interaction times, relaxation times and phases.
The quantized excited energy is about 6.4 k = 0.55meV. | cond-mat_dis-nn |
Biased doped silicene as a source for advanced electronics: Restructuring of electronic spectrum in a buckled silicene monolayer under
some applied voltage between its two sublattices and in presence of certain
impurity atoms is considered. A special attention is given to formation of
localized impurity levels within the band gap and the to their collectivization
at finite impurity concentration. It is shown that a qualitative restructuring
of quasiparticle spectrum within the initial band gap and then specific
metal-insulator phase transitions are possible for such disordered system and
can be effectively controlled by variation of the electric field bias at given
impurity perturbation potential and concentration. Since these effects are
expected at low impurity concentrations but at not too low temperatures, they
can be promising for practical applications in nanoelectronics devices. | cond-mat_dis-nn |
Eigenstate phases with finite on-site non-Abelian symmetry: We study the eigenstate phases of disordered spin chains with on-site finite
non-Abelian symmetry. We develop a general formalism based on standard group
theory to construct local spin Hamiltonians invariant under any on-site
symmetry. We then specialize to the case of the simplest non-Abelian group,
$S_3$, and numerically study a particular two parameter spin-1 Hamiltonian. We
observe a thermal phase and a many-body localized phase with a spontaneous
symmetry breaking (SSB) from $S_3$ to $\mathbb{Z}_3$ in our model Hamiltonian.
We diagnose these phases using full entanglement distributions and level
statistics. We also use a spin-glass diagnostic specialized to detect
spontaneous breaking of the $S_3$ symmetry down to $\mathbb{Z}_3$. Our observed
phases are consistent with the possibilities outlined by Potter and Vasseur
[Phys. Rev. B 94, 224206 (2016)], namely thermal/ ergodic and spin-glass
many-body localized (MBL) phases. We also speculate about the nature of an
intermediate region between the thermal and MBL+SSB regions where full $S_3$
symmetry exists. | cond-mat_dis-nn |
The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses
Supports Replica Symmetry Breaking: We present a general and powerful numerical method useful to study the
density matrix of spin models. We apply the method to finite dimensional spin
glasses, and we analyze in detail the four dimensional Edwards-Anderson model
with Gaussian quenched random couplings. Our results clearly support the
existence of replica symmetry breaking in the thermodynamical limit. | cond-mat_dis-nn |
Topological phase transitions in random Kitaev $α$-chains: The topological phases of random Kitaev $\alpha$-chains are labelled by the
number of localized edge Majorana Zero Modes. The critical lines between these
phases thus correspond to delocalization transitions for these localized edge
Majorana Zero Modes. For the random Kitaev chain with next-nearest couplings,
where there are three possible topological phases $n=0,1,2$, the two Lyapunov
exponents of Majorana Zero Modes are computed for a specific solvable case of
Cauchy disorder, in order to analyze how the phase diagram evolves as a
function of the disorder strength. In particular, the direct phase transition
between the phases $n=0$ and $n=2$ is possible only in the absence of disorder,
while the presence of disorder always induces an intermediate phase $n=1$, as
found previously via numerics for other distributions of disorder. | cond-mat_dis-nn |
Strong Griffiths singularities in random systems and their relation to
extreme value statistics: We consider interacting many particle systems with quenched disorder having
strong Griffiths singularities, which are characterized by the dynamical
exponent, z, such as random quantum systems and exclusion processes. In several
d=1 and d=2 dimensional problems we have calculated the inverse time-scales,
t^{-1}, in finite samples of linear size, L, either exactly or numerically. In
all cases, having a discrete symmetry, the distribution function, P(t^{-1},L),
is found to depend on the variable, u=t^{-1}L^{z/d}, and to be universal given
by the limit distribution of extremes of independent and identically
distributed random numbers. This finding is explained in the framework of a
strong disorder renormalization group approach when, after fast degrees of
freedom are decimated out the system is transformed into a set of
non-interacting localized excitations. The Frechet distribution of P(t^{-1},L)
is expected to hold for all random systems having a strong disorder fixed
point, in which the Griffiths singularities are dominated by disorder
fluctuations. | cond-mat_dis-nn |
Diluted neural networks with adapting and correlated synapses: We consider the dynamics of diluted neural networks with clipped and adapting
synapses. Unlike previous studies, the learning rate is kept constant as the
connectivity tends to infinity: the synapses evolve on a time scale
intermediate between the quenched and annealing limits and all orders of
synaptic correlations must be taken into account. The dynamics is solved by
mean-field theory, the order parameter for synapses being a function. We
describe the effects, in the double dynamics, due to synaptic correlations. | cond-mat_dis-nn |
Machine learning magnetic parameters from spin configurations: Hamiltonian parameter estimation is crucial in condensed matter physics, but
time and cost consuming in terms of resources used. With advances in
observation techniques, high-resolution images with more detailed information
are obtained, which can serve as an input to machine learning (ML) algorithms
to extract Hamiltonian parameters. However, the number of labeled images is
rather limited. Here, we provide a protocol for Hamiltonian parameter
estimation based on a machine learning architecture, which is trained on a
small amount of simulated images and applied to experimental spin configuration
images. Sliding windows on the input images enlarges the number of training
images; therefore we can train well a neural network on a small dataset of
simulated images which are generated adaptively using the same external
conditions such as temperature and magnetic field as the experiment. The neural
network is applied to the experimental image and estimates magnetic parameters
efficiently. We demonstrate the success of the estimation by reproducing the
same configuration from simulation and predict a hysteresis loop accurately.
Our approach paves a way to a stable and general parameter estimation. | cond-mat_dis-nn |
A Green's function approach to transmission of massless Dirac fermions
in graphene through an array of random scatterers: We consider the transmission of massless Dirac fermions through an array of
short range scatterers which are modeled as randomly positioned $\delta$-
function like potentials along the x-axis. We particularly discuss the
interplay between disorder-induced localization that is the hallmark of a
non-relativistic system and two important properties of such massless Dirac
fermions, namely, complete transmission at normal incidence and periodic
dependence of transmission coefficient on the strength of the barrier that
leads to a periodic resonant transmission. This leads to two different types of
conductance behavior as a function of the system size at the resonant and the
off-resonance strengths of the delta function potential. We explain this
behavior of the conductance in terms of the transmission through a pair of such
barriers using a Green's function based approach. The method helps to
understand such disordered transport in terms of well known optical phenomena
such as Fabry Perot resonances. | cond-mat_dis-nn |
Absence of Mobility Edge in Short-range Uncorrelated Disordered Model:
Coexistence of Localized and Extended States: Unlike the well-known Mott's argument that extended and localized states
should not coexist at the same energy in a generic random potential, we provide
an example of a nearest-neighbor tight-binding disordered model which carries
both localized and extended states without forming the mobility edge (ME).
Unexpectedly, this example appears to be given by a well-studied
$\beta$-ensemble with independently distributed random diagonal potential and
inhomogeneous kinetic hopping terms. In order to analytically tackle the
problem, we locally map the above model to the 1D Anderson model with
matrix-size- and position-dependent hopping and confirm the coexistence of
localized and extended states, which is shown to be robust to the perturbations
of both potential and kinetic terms due to the separation of the above states
in space. In addition, the mapping shows that the extended states are
non-ergodic and allows to analytically estimate their fractal dimensions. | cond-mat_dis-nn |
Competition between Barrier- and Entropy-Driven Activation in Glasses: In simplified models of glasses we clarify the existence of two different
kinds of activated dynamics, which coexist, with one of the two dominating over
the other. One is the energy barrier hopping that is typically used to picture
activation, and the other one, which we call entropic activation, is driven by
the scarcity of convenient directions. When entropic activation dominates, the
height of the energy barriers is no longer the decisive to describe the
system's slowdown. In our analysis, dominance of one mechanism over the other
depends on the shape of the density of states and temperature. We also find
that at low temperatures a phase transition between the two kinds of activation
can occur. Our framework can be used to harmonize the facilitation and
thermodynamic pictures of the slowdown of glasses. | cond-mat_dis-nn |
Non-equilibrium criticality and efficient exploration of glassy
landscapes with memory dynamics: Spin glasses are notoriously difficult to study both analytically and
numerically due to the presence of frustration and metastability. Their highly
non-convex landscapes require collective updates to explore efficiently.
Currently, most state-of-the-art algorithms rely on stochastic spin clusters to
perform non-local updates, but such "cluster algorithms" lack general
efficiency. Here, we introduce a non-equilibrium approach for simulating spin
glasses based on classical dynamics with memory. By simulating various classes
of 3d spin glasses (Edwards-Anderson, partially-frustrated, and
fully-frustrated models), we find that memory dynamically promotes critical
spin clusters during time evolution, in a self-organizing manner. This
facilitates an efficient exploration of the low-temperature phases of spin
glasses. | cond-mat_dis-nn |
Quantum dynamics in strongly driven random dipolar magnets: The random dipolar magnet LiHo$_x$Y$_{1-x}$F$_4$ enters a strongly frustrated
regime for small Ho$^{3+}$ concentrations with $x<0.05$. In this regime, the
magnetic moments of the Ho$^{3+}$ ions experience small quantum corrections to
the common Ising approximation of LiHo$_x$Y$_{1-x}$F$_4$, which lead to a
$Z_2$-symmetry breaking and small, degeneracy breaking energy shifts between
different eigenstates. Here we show that destructive interference between two
almost degenerate excitation pathways burns spectral holes in the magnetic
susceptibility of strongly driven magnetic moments in LiHo$_x$Y$_{1-x}$F$_4$.
Such spectral holes in the susceptibility, microscopically described in terms
of Fano resonances, can already occur in setups of only two or three frustrated
moments, for which the driven level scheme has the paradigmatic
$\Lambda$-shape. For larger clusters of magnetic moments, the corresponding
level schemes separate into almost isolated many-body $\Lambda$-schemes, in the
sense that either the transition matrix elements between them are negligibly
small or the energy difference of the transitions is strongly off-resonant to
the drive. This enables the observation of Fano resonances, caused by many-body
quantum corrections to the common Ising approximation also in the thermodynamic
limit. We discuss its dependence on the driving strength and frequency as well
as the crucial role that is played by lattice dissipation. | cond-mat_dis-nn |
Phase boundary near a magnetic percolation transition: Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)]
on hexagonal ferrites, we revisit the phase diagrams of diluted magnets close
to the lattice percolation threshold. We perform large-scale Monte Carlo
simulations of XY and Heisenberg models on both simple cubic lattices and
lattices representing the crystal structure of the hexagonal ferrites. Close to
the percolation threshold $p_c$, we find that the magnetic ordering temperature
$T_c$ depends on the dilution $p$ via the power law $T_c \sim |p-p_c|^\phi$
with exponent $\phi=1.09$, in agreement with classical percolation theory.
However, this asymptotic critical region is very narrow, $|p-p_c| \lesssim
0.04$. Outside of it, the shape of the phase boundary is well described, over a
wide range of dilutions, by a nonuniversal power law with an exponent somewhat
below unity. Nonetheless, the percolation scenario does not reproduce the
experimentally observed relation $T_c \sim (x_c -x)^{2/3}$ in
PbFe$_{12-x}$Ga$_x$O$_{19}$. We discuss the generality of our findings as well
as implications for the physics of diluted hexagonal ferrites. | cond-mat_dis-nn |
Fidelity susceptibility in Gaussian Random Ensembles: The fidelity susceptibility measures sensitivity of eigenstates to a change
of an external parameter. It has been fruitfully used to pin down quantum phase
transitions when applied to ground states (with extensions to thermal states).
Here we propose to use the fidelity susceptibility as a useful dimensionless
measure for complex quantum systems. We find analytically the fidelity
susceptibility distributions for Gaussian orthogonal and unitary universality
classes for arbitrary system size. The results are verified by a comparison
with numerical data. | cond-mat_dis-nn |
Universality of phonon transport in surface-roughness dominated
nanowires: We analyze, both theoretically and numerically, the temperature dependent
thermal conductivity \k{appa} of two-dimensional nanowires with surface
roughness. Although each sample is characterized by three independent
parameters - the diameter (width) of the wire, the correlation length and
strength of the surface corrugation - our theory predicts that there exists a
universal regime where \k{appa} is a function of a single combination of all
three model parameters. Numerical simulations of propagation of acoustic
phonons across thin wires confirm this universality and predict a d 1/2
dependence of \k{appa} on the diameter d. | cond-mat_dis-nn |
A glassy phase in quenched disordered graphene and crystalline membranes: We investigate the flat phase of $D$-dimensional crystalline membranes
embedded in a $d$-dimensional space and submitted to both metric and curvature
quenched disorders using a nonperturbative renormalization group approach. We
identify a second order phase transition controlled by a finite-temperature,
finite-disorder fixed point unreachable within the leading order of
$\epsilon=4-D$ and $1/d$ expansions. This critical point divides the flow
diagram into two basins of attraction: that associated to the
finite-temperature fixed point controlling the long distance behaviour of
disorder-free membranes and that associated to the zero-temperature,
finite-disorder fixed point. Our work thus strongly suggests the existence of a
whole low-temperature glassy phase for quenched disordered graphene,
graphene-like compounds and, more generally, crystalline membranes. | cond-mat_dis-nn |
Possibly Exact Solution for the Multicritical Point of
Finite-Dimensional Spin Glasses: After briefly describing the present status of the spin glass theory, we
present a conjecture on the exact location of the multicritical point in the
phase diagram of finite-dimensional spin glasses. The theory enables us to
understand in a unified way many numerical results for two-, three- and
four-dimensional models including the +-J Ising model, random Potts model,
random lattice gauge theory, and random Zq model. It is also suggested from the
same theoretical framework that models with symmetric distribution of
randomness in exchange interaction have no finite-temperature transition on the
square lattice. | cond-mat_dis-nn |
Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder
systems: One-Particle Properties and Boundary Effects: Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized
by a gap in the spin-excitation spectrum, which can be modeled at low energies
by that of Dirac fermions with a mass. In the presence of disorder these
systems can still be described by a Dirac fermion model, but with a random
mass. Some peculiar properties, like the Dyson singularity in the density of
states, are well known and attributed to creation of low-energy states due to
the disorder. We take one step further and study single-particle correlations
by means of Berezinskii's diagram technique. We find that, at low energy
$\epsilon$, the single-particle Green function decays in real space like
$G(x,\epsilon) \propto (1/x)^{3/2}$. It follows that at these energies the
correlations in the disordered system are strong -- even stronger than in the
pure system without the gap. Additionally, we study the effects of boundaries
on the local density of states. We find that the latter is logarithmically (in
the energy) enhanced close to the boundary. This enhancement decays into the
bulk as $1/\sqrt{x}$ and the density of states saturates to its bulk value on
the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from
the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. We
also discuss some implications of these results for the spin systems and their
relation to the investigations based on real-space renormalization group
approach. | cond-mat_dis-nn |
Finite-size corrections in the random assignment problem: We analytically derive, in the context of the replica formalism, the first
finite size corrections to the average optimal cost in the random assignment
problem for a quite generic distribution law for the costs. We show that, when
moving from a power-law distribution to a $\Gamma$ distribution, the leading
correction changes both in sign and in its scaling properties. We also examine
the behavior of the corrections when approaching a $\delta$-function
distribution. By using a numerical solution of the saddle-point equations, we
provide predictions that are confirmed by numerical simulations. | cond-mat_dis-nn |
Temperature-dependent disorder and magnetic field driven disorder:
experimental observations for doped GaAs/AlGaAs quantum well structures: We report experimental studies of conductance and magnetoconductance of
GaAs/AlGaAs quantum well structures where both wells and barriers are doped by
acceptor impurity Be. Temperature dependence of conductance demonstrate a
non-monotonic behavior at temperatures around 100 K. At small temperatures
(less than 10 K) we observed strong negative magnetoresistance at moderate
magnetic field which crossed over to positive magnetoresistance at very strong
magnetic fields and was completely suppressed with an increase of temperature.
We ascribe these unusual features to effects of temperature and magnetic field
on a degree of disorder. The temperature dependent disorder is related to
charge redistribution between different localized states with an increase of
temperature. The magnetic field dependent disorder is also related by charge
redistribution between different centers, however in this case an important
role is played by the doubly occupied states of the upper Hubbard band, their
occupation being sensitive to magnetic field due to on-site spin correlations.
The detailed theoretical model is present. | cond-mat_dis-nn |
T=0 phase diagram and nature of domains in ultrathin ferromagnetic films
with perpendicular anisotropy: We present the complete zero temperature phase diagram of a model for
ultrathin films with perpendicular anisotropy. The whole parameter space of
relevant coupling constants is studied in first order anisotropy approximation.
Because the ground state is known to be formed by perpendicular stripes
separated by Bloch walls, a standard variational approach is used, complemented
with specially designed Monte Carlo simulations. We can distinguish four
regimes according to the different nature of striped domains: a high anisotropy
Ising regime with sharp domain walls, a saturated stripe regime with thicker
walls inside which an in-plane component of the magnetization develops, a
narrow canted-like regime, characterized by a sinusoidal variation of both the
in-plane and the out of plane magnetization components, which upon further
decrease of the anisotropy leads to an in-plane ferromagnetic state via a spin
reorientation transition (SRT). The nature of domains and walls are described
in some detail together with the variation of domain width with anisotropy, for
any value of exchange and dipolar interactions. Our results, although strictly
valid at $T=0$, can be valuable for interpreting data on the evolution of
domain width at finite temperature, a still largely open problem. | cond-mat_dis-nn |
Normal mode analysis of spectra of random networks: Several spectral fluctuation measures of random matrix theory (RMT) have been
applied in the study of spectral properties of networks. However, the
calculation of those statistics requires performing an unfolding procedure,
which may not be an easy task. In this work, network spectra are interpreted as
time series, and we show how their short and long-range correlations can be
characterized without implementing any previous unfolding. In particular, we
consider three different representations of Erd\"os-R\'enyi (ER) random
networks: standard ER networks, ER networks with random-weighted self-edges,
and fully random-weighted ER networks. In each case, we apply singular value
decomposition (SVD) such that the spectra are decomposed in trend and
fluctuation normal modes. We obtain that the fluctuation modes exhibit a clear
crossover between the Poisson and the Gaussian orthogonal ensemble statistics
when increasing the average degree of ER networks. Moreover, by using the trend
modes, we perform a data-adaptive unfolding to calculate, for comparison
purposes, traditional fluctuation measures such as the nearest neighbor spacing
distribution, number variance $\Sigma$2, as well as $\Delta$3 and {\delta}n
statistics. The thorough comparison of RMT short and long-range correlation
measures make us identify the SVD method as a robust tool for characterizing
random network spectra. | cond-mat_dis-nn |
The Approximate Invariance of the Average Number of Connections for the
Continuum Percolation of Squares at Criticality: We perform Monte Carlo simulations to determine the average excluded area
$<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and
aligned squares in two dimensions. We find significant differences between our
results for randomly oriented squares and previous analytical results for the
same. The sources of these differences are explained. Using our results for
$<A_{ex}>$ and Monte Carlo simulation results for the percolation threshold, we
estimate the mean number of connections per object $B_c$ at the percolation
threshold for squares in 2-D. We study systems of squares that are allowed
random orientations within a specified angular interval. Our simulations show
that the variation in $B_c$ is within 1.6% when the angular interval is varied
from 0 to $\pi/2$. | cond-mat_dis-nn |
Backtracking Dynamical Cavity Method: The cavity method is one of the cornerstones of the statistical physics of
disordered systems such as spin glasses and other complex systems. It is able
to analytically and asymptotically exactly describe the equilibrium properties
of a broad range of models. Exact solutions for dynamical, out-of-equilibrium
properties of disordered systems are traditionally much harder to obtain. Even
very basic questions such as the limiting energy of a fast quench are so far
open. The dynamical cavity method partly fills this gap by considering short
trajectories and leveraging the static cavity method. However, being limited to
a couple of steps forward from the initialization it typically does not capture
dynamical properties related to attractors of the dynamics. We introduce the
backtracking dynamical cavity method that instead of analysing the trajectory
forward from initialization, analyses trajectories that are found by tracking
them backward from attractors. We illustrate that this rather elementary twist
on the dynamical cavity method leads to new insight into some of the very basic
questions about the dynamics of complex disordered systems. This method is as
versatile as the cavity method itself and we hence anticipate that our paper
will open many avenues for future research of dynamical, out-of-equilibrium,
properties in complex systems. | cond-mat_dis-nn |
Low-frequency vibrational spectrum of mean-field disordered systems: We study a recently introduced and exactly solvable mean-field model for the
density of vibrational states $\mathcal{D}(\omega)$ of a structurally
disordered system. The model is formulated as a collection of disordered
anharmonic oscillators, with random stiffness $\kappa$ drawn from a
distribution $p(\kappa)$, subjected to a constant field $h$ and interacting
bilinearly with a coupling of strength $J$. We investigate the vibrational
properties of its ground state at zero temperature. When $p(\kappa)$ is gapped,
the emergent $\mathcal{D}(\omega)$ is also gapped, for small $J$. Upon
increasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase
diagram, whereupon replica symmetry is broken. At small $h$, the form of this
pseudogap is quadratic, $\mathcal{D}(\omega)\sim\omega^2$, and its modes are
delocalized, as expected from previously investigated mean-field spin glass
models. However, we determine that for large enough $h$, a quartic pseudogap
$\mathcal{D}(\omega)\sim\omega^4$, populated by localized modes, emerges, the
two regimes being separated by a special point on the critical line. We thus
uncover that mean-field disordered systems can generically display both a
quadratic-delocalized and a quartic-localized spectrum at the glass transition. | cond-mat_dis-nn |
A Complex Network Analysis on The Eigenvalue Spectra of Random Spin
Systems: Recent works have established a novel viewpoint that treats the eigenvalue
spectra of disordered quantum systems as time-series, and corresponding
algorithms such as singular-value-decomposition has proven its advantage in
studying subtle physical quantities like Thouless energy and non-ergodic
extended regime. On the other hand, algorithms from complex networks have long
been known as a powerful tool to study highly nonlinear time-series. In this
work, we combine these two ideas together. Using the particular algorithm
called visibility graph (VG) that transforms the eigenvalue spectra of a random
spin system into complex networks, it's shown the degree distribution of the
resulting network is capable of signaturing the eigenvalue evolution during the
thermal to many-body localization transition, and the networks in the thermal
phase have a small-world structure. We further show these results are robust
even when the eigenvalues are incomplete with missing levels, which reveals the
advantage of the VG algorithm. | cond-mat_dis-nn |
Analyses of kinetic glass transition in short-range attractive colloids
based on time-convolutionless mode-coupling theory: The kinetic glass transition in short-range attractive colloids is
theoretically studied by time-convolutionless mode-coupling theory (TMCT). By
numerical calculations, TMCT is shown to recover all the remarkable features
predicted by the mode-coupling theory for attractive colloids, namely the
glass-liquid-glass reentrant, the glass-glass transition, and the higher-order
singularities. It is also demonstrated through the comparisons with the results
of molecular dynamics for the binary attractive colloids that TMCT improves the
critical values of the volume fraction. In addition, a schematic model of three
control parameters is investigated analytically. It is thus confirmed that TMCT
can describe the glass-glass transition and higher-order singularities even in
such a schematic model. | cond-mat_dis-nn |
Maximum-energy records in glassy energy landscapes: We study the evolution of the maximum energy $E_\max(t)$ reached between time
$0$ and time $t$ in the dynamics of simple models with glassy energy
landscapes, in instant quenches from infinite temperature to a target
temperature $T$. Through a detailed description of the activated dynamics, we
are able to describe the evolution of $E_\max(t)$ from short times, through the
aging regime, until after equilibrium is reached, thus providing a detailed
description of the long-time dynamics. Finally, we compare our findings with
numerical simulations of the $p$-spin glass and show how the maximum energy
record can be used to identify the threshold energy in this model. | cond-mat_dis-nn |
Destruction of Localization by Thermal Inclusions: Anomalous Transport
and Griffiths Effects in the Anderson and André-Aubry-Harper Models: We discuss and compare two recently proposed toy models for anomalous
transport and Griffiths effects in random systems near the Many-Body
Localization transitions: the random dephasing model, which adds thermal
inclusions in an Anderson Insulator as local Markovian dephasing channels that
heat up the system, and the random Gaussian Orthogonal Ensemble (GOE) approach
which models them in terms of ensembles of random regular graphs. For these two
settings we discuss and compare transport and dissipative properties and their
statistics. We show that both types of dissipation lead to similar
Griffiths-like phenomenology, with the GOE bath being less effective in
thermalising the system due to its finite bandwidth. We then extend these
models to the case of a quasi-periodic potential as described by the
Andr\'e-Aubry-Harper model coupled to random thermal inclusions, that we show
to display, for large strength of the quasiperiodic potential, a similar
phenomenology to the one of the purely random case. In particular, we show the
emergence of subdiffusive transport and broad statistics of the local density
of states, suggestive of Griffiths like effects arising from the interplay
between quasiperiodic localization and random coupling to the baths. | cond-mat_dis-nn |
A frozen glass phase in the multi-index matching problem: The multi-index matching is an NP-hard combinatorial optimization problem;
for two indices it reduces to the well understood bipartite matching problem
that belongs to the polynomial complexity class. We use the cavity method to
solve the thermodynamics of the multi-index system with random costs. The phase
diagram is much richer than for the case of the bipartite matching problem: it
shows a finite temperature phase transition to a completely frozen glass phase,
similar to what happens in the random energy model. We derive the critical
temperature, the ground state energy density, and properties of the energy
landscape, and compare the results to numerical studies based on exact analysis
of small systems. | cond-mat_dis-nn |
Spatio-temporal heterogeneity of entanglement in many-body localized
systems: We propose a spatio-temporal characterization of the entanglement dynamics in
many-body localized (MBL) systems, which exhibits a striking resemblance with
dynamical heterogeneity in classical glasses. Specifically, we find that the
relaxation times of local entanglement, as measured by the concurrence, are
spatially correlated yielding a dynamical length scale for quantum
entanglement. As a consequence of this spatio-temporal analysis, we observe
that the considered MBL system is made up of dynamically correlated clusters
with a size set by this entanglement length scale. The system decomposes into
compartments of different activity such as active regions with fast quantum
entanglement dynamics and inactive regions where the dynamics is slow. We
further find that the relaxation times of the on-site concurrence become
broader distributed and more spatially correlated, as disorder increases or the
energy of the initial state decreases. Through this spatio-temporal
characterization of entanglement, our work unravels a previously unrecognized
connection between the behavior of classical glasses and the genuine quantum
dynamics of MBL systems. | cond-mat_dis-nn |
Resistance distribution in the hopping percolation model: We study the distribution function, P(rho), of the effective resistance, rho,
in two and three-dimensional random resistor network of linear size L in the
hopping percolation model. In this model each bond has a conductivity taken
from an exponential form \sigma ~ exp(-kappa r), where kappa is a measure of
disorder, and r is a random number, 0< r < 1. We find that in both the usual
strong disorder regime L/kappa^{nu} > 1 (not sensitive to removal of any single
bond) and the extreme disorder regime L/kappa^{nu} < 1 (very sensitive to such
a removal) the distribution depends only on L/kappa^{nu} and can be well
approximated by a log-normal function with dispersion b kappa^nu/L, where b is
a coefficient which depends on the type of the lattice | cond-mat_dis-nn |
Coupled electron--heat transport in nonuniform thin film semiconductor
structures: A theory of transverse electron transport coupled with heat transfer in
semiconductor thin films is developed conceptually modeling structures of
modern electronics. The transverse currents generate Joule heat with positive
feedback through thermally activated conductivity. This can lead to instability
known as thermal runaway, or hot spot, or reversible thermal breakdown. A
theory here is based on the optimum fluctuation method modified to describe
saddle stationary points determining the rate of such instabilities and
conditions under which they evolve. Depending on the material and system
parameters, the instabilities appear in a manner of phase transitions, similar
to either nucleation or spinodal decomposition. | cond-mat_dis-nn |
Depinning exponents of the driven long-range elastic string: We perform a high-precision calculation of the critical exponents for the
long-range elastic string driven through quenched disorder at the depinning
transition, at zero temperature. Large-scale simulations are used to avoid
finite-size effects and to enable high precision. The roughness, growth, and
velocity exponents are calculated independently, and the dynamic and
correlation length exponents are derived. The critical exponents satisfy known
scaling relations and agree well with analytical predictions. | cond-mat_dis-nn |
Scale Invariance in Percolation Theory and Fractals: The properties of the similarity transformation in percolation theory in the
complex plane of the percolation probability are studied. It is shown that the
percolation problem on a two-dimensional square lattice reduces to the
Mandelbrot transformation, leading to a fractal behavior of the percolation
probability in the complex plane. The hierarchical chains of impedances,
reducing to a nonlinear mapping of the impedance space onto itself, are
studied. An infinite continuation of the procedure leads to a fixed point. It
is shown that the number of steps required to reach a neighborhood of this
point has a fractal distribution. | cond-mat_dis-nn |
Rapid algorithm for identifying backbones in the two-dimensional
percolation model: We present a rapid algorithm for identifying the current-carrying backbone in
the percolation model. It applies to general two-dimensional graphs with open
boundary conditions. Complemented by the modified Hoshen-Kopelman cluster
labeling algorithm, our algorithm identifies dangling parts using their local
properties. For planar graphs, it finds the backbone almost four times as fast
as Tarjan's depth-first-search algorithm, and uses the memory of the same size
as the modified Hoshen-Kopelman algorithm. Comparison with other algorithms for
backbone identification is addressed. | cond-mat_dis-nn |
Short-Range Spin Glasses: The Metastate Approach: We discuss the metastate, a probability measure on thermodynamic states, and
its usefulness in addressing difficult questions pertaining to the statistical
mechanics of systems with quenched disorder, in particular short-range spin
glasses. The possible low-temperature structures of realistic (i.e.,
short-range) spin glass models are described, and a number of fundamental open
questions are presented. | cond-mat_dis-nn |
How to guess the inter magnetic bubble potential by using a simple
perceptron ?: It is shown that magnetic bubble films behaviour can be described by using a
2D super-Ising hamiltonian. Calculated hysteresis curves and magnetic domain
patterns are successfully compared with experimental results taken in
literature. The reciprocal problem of finding paramaters of the super-Ising
model to reproduce computed or experimental magnetic domain pictures is solved
by using a perceptron neural network. | cond-mat_dis-nn |
Kovacs effect in solvable model glasses: The Kovacs protocol, based on the temperature shift experiment originally
conceived by A.J. Kovacs and applied on glassy polymers, is implemented in an
exactly solvable model with facilitated dynamics. This model is based on
interacting fast and slow modes represented respectively by spherical spins and
harmonic oscillator variables. Due to this fundamental property and to slow
dynamics, the model reproduces the characteristic non-monotonic evolution known
as the ``Kovacs effect'', observed in polymers, spin glasses, in granular
materials and models of molecular liquids, when similar experimental protocols
are implemented. | cond-mat_dis-nn |
Non-equilibrium physics: from spin glasses to machine and neural
learning: Disordered many-body systems exhibit a wide range of emergent phenomena
across different scales. These complex behaviors can be utilized for various
information processing tasks such as error correction, learning, and
optimization. Despite the empirical success of utilizing these systems for
intelligent tasks, the underlying principles that govern their emergent
intelligent behaviors remain largely unknown. In this thesis, we aim to
characterize such emergent intelligence in disordered systems through
statistical physics. We chart a roadmap for our efforts in this thesis based on
two axes: learning mechanisms (long-term memory vs. working memory) and
learning dynamics (artificial vs. natural). Throughout our journey, we uncover
relationships between learning mechanisms and physical dynamics that could
serve as guiding principles for designing intelligent systems. We hope that our
investigation into the emergent intelligence of seemingly disparate learning
systems can expand our current understanding of intelligence beyond neural
systems and uncover a wider range of computational substrates suitable for AI
applications. | cond-mat_dis-nn |
On Renyi entropies characterizing the shape and the extension of the
phase space representation of quantum wave functions in disordered systems: We discuss some properties of the generalized entropies, called Renyi
entropies and their application to the case of continuous distributions. In
particular it is shown that these measures of complexity can be divergent,
however, their differences are free from these divergences thus enabling them
to be good candidates for the description of the extension and the shape of
continuous distributions. We apply this formalism to the projection of wave
functions onto the coherent state basis, i.e. to the Husimi representation. We
also show how the localization properties of the Husimi distribution on average
can be reconstructed from its marginal distributions that are calculated in
position and momentum space in the case when the phase space has no structure,
i.e. no classical limit can be defined. Numerical simulations on a one
dimensional disordered system corroborate our expectations. | cond-mat_dis-nn |
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