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arXiv2014

Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models

We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin ladder. A subsequent analysis of the superspin ladder and the corresponding supersymmetric nonlinear sigma model allows to establish the phase diagram of the network model, and the form of the critical line of the weak-field IQH transition. Our results confirm the universality of the IQH transition, which is described by the same sigma model in strong and weak magnetic fields. We apply the suspersymmetry method to several related network models that were introduced in the literature to describe the quantum Hall effect in graphene, the spin-degenerate Landau levels, and localization of electrons in a random magnetic field.

cond-mat.dis-nn↗

arXiv2017

Refining glass structure in two dimensions

Recently determined atomistic scale structures of near-two dimensional bilayers of vitreous silica (using scanning probe and electron microscopy) allow us to refine the experimentally determined coordinates to incorporate the known local chemistry more precisely. Further refinement is achieved by using classical potentials of varying complexity; one using harmonic potentials and the second employing an electrostatic description incorporating polarization effects. These are benchmarked against density functional calculations. Our main findings are that (a) there is a symmetry plane between the two disordered layers; a nice example of an emergent phenomenon, (b) the layers are slightly tilted so that the Si-O-Si angle between the two layers is not $180^{\circ}$ as originally thought but rather $175 \pm 2 ^{\circ}$ and (c) while interior areas that are not completely imagined can be reliably reconstructed, surface areas are more problematical. It is shown that small crystallites that appear are just as expected statistically in a continuous random network. This provides a good example of the value that can be added to disordered structures imaged at the atomic level by implementing computer refinement.

cond-mat.dis-nn↗

arXiv2018

Quantum algorithm for energy matching in hard optimization problems

We consider the ability of local quantum dynamics to solve the energy matching problem: given an instance of a classical optimization problem and a low energy state, find another macroscopically distinct low energy state. Energy matching is difficult in rugged optimization landscapes, as the given state provides little information about the distant topography. Here we show that the introduction of quantum dynamics can provide a speed-up over local classical algorithms in a large class of hard optimization problems. The essential intuition is that tunneling allows the system to explore the optimization landscape while approximately conserving the classical energy, even in the presence of large barriers. In particular, we study energy matching in the random p-spin model of spin glass theory. Using perturbation theory and numerical exact diagonalization, we show that introducing a transverse field leads to three sharp dynamical phases, only one of which solves the matching problem: (1) a small-field trapped phase, in which tunneling is too weak for the system to escape the vicinity of the initial state; (2) a large-field excited phase, in which the field excites the system into high energy states, effectively forgetting the initial low energy; and (3) the intermediate tunneling phase, in which the system succeeds at energy matching. We find that in the tunneling phase, the time required to find distant states scales exponentially with system size but is nevertheless exponentially faster than simple classical Monte Carlo.

cond-mat.dis-nn↗

arXiv2012

Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra

Motivated by the statistical fluctuation of Dirac spectrum of QCD-like theories subjected to (pseudo)reality-violating perturbations and in the epsilon-regime, we compute the smallest eigenvalue distribution and the level spacing distribution of chiral and non-chiral parametric random matrix ensembles of Dyson-Mehta-Pandey type. To this end we employ the Nystrom method to numerically evaluate the Fredholm Pfaffian of the integral kernel for the chG(O,S)E-chGUE and G(O,S)E-GUE crossover. We confirm the validity and universality of our results by comparing them with several lattice models, namely fundamental and adjoint staggered Dirac spectra of SU(2) quenched lattice gauge theory under the twisted boundary condition (imaginary chemical potential) or perturbed by phase noise. Both in the zero-virtuality region and in the spectral bulk, excellent one-parameter fitting is achieved already on a small 4^4 lattice. Anticipated scaling of the fitting parameter with the twisting phase, mean level spacing, and the system size allows for precise determination of the pion decay (diffusion) constant F in the low-energy effective Lagrangian.

hep-lat↗

arXiv2012

Poisson to Random Matrix Transition in the QCD Dirac Spectrum

At zero temperature the lowest part of the spectrum of the QCD Dirac operator is known to consist of delocalized modes that are described by random matrix statistics. In the present paper we show that the nature of these eigenmodes changes drastically when the system is driven through the finite temperature cross-over. The lowest Dirac modes that are delocalized at low temperature become localized on the scale of the inverse temperature. At the same time the spectral statistics changes from random matrix to Poisson statistics. We demonstrate this with lattice QCD simulations using 2+1 flavors of light dynamical quarks with physical masses. Drawing an analogy with Anderson transitions we also examine the mobility edge separating localized and delocalized modes in the spectrum. We show that it scales in the continuum limit and increases sharply with the temperature.

hep-lat↗

arXiv2022

Exotic states induced by co-evolving connection weights and phases in complex networks

We consider an adaptive network, whose connection weights co-evolve in congruence with the dynamical states of the local nodes that are under the influence of an external stimulus. The adaptive dynamical system mimics the adaptive synaptic connections common in neuronal networks. The adaptive network under external forcing displays exotic dynamical states such as itinerant chimeras whose population density of coherent and incoherent domains co-evolves with the synaptic connection, bump states and bump frequency cluster states, which do not exist in adaptive networks without forcing. In addition the adaptive network also exhibits partial synchronization patterns such as phase and frequency clusters, forced entrained, and incoherent states. We introduce two measures for the strength of incoherence based on the standard deviation of the temporally averaged (mean) frequency and on the mean frequency in order to classify the emergent dynamical states as well as their transitions. We provide a two-parameter phase diagram showing the wealth of dynamical states. We additionally deduce the stability condition for the frequency-entrained state. We use the paradigmatic Kuramoto model of phase oscillators which is a simple generic model that has been widely employed in unraveling a plethora of cooperative phenomena in natural and man-made systems.

cond-mat.dis-nn↗

arXiv2024

Nonequilbrium physics of generative diffusion models

Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interests from engineering, statistics and physics, but a complete picture about inherent mechanisms is still lacking. In this paper, we provide a transparent physics analysis of diffusion models, formulating the fluctuation theorem, entropy production, equilibrium measure, and Franz-Parisi potential to understand the dynamic process and intrinsic phase transitions. Our analysis is rooted in a path integral representation of both forward and backward dynamics, and in treating the reverse diffusion generative process as a statistical inference, where the time-dependent state variables serve as quenched disorder akin to that in spin glass theory. Our study thus links stochastic thermodynamics, statistical inference and geometry based analysis together to yield a coherent picture about how the generative diffusion models work.

cond-mat.stat-mech↗

arXiv2011

Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural entropy obtained by computing the approximate entropy of the so called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdős-Rényi networks. By using classical results of Pincus, we show that our entropy measure converges with network size to a certain binary Shannon entropy. On a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs permit to naturally associate to a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

cond-mat.dis-nn↗

arXiv2012

Is transport in time-dependent random potentials universal ?

The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small velocities uniform acceleration takes place, and at a later stage fluctuations of the potential are encountered, resulting in a regime of anomalous diffusion. This regime was studied in the framework of the Fokker-Planck approximation. The diffusion coefficient in velocity was expressed in terms of the average power spectral density, which is the Fourier transform of the potential correlation function. This enabled to establish a scaling form for the Fokker-Planck equation and to compute the large and small velocity limits of the diffusion coefficient. A classification of the random potentials into universality classes, characterized by the form of the diffusion coefficient in the limit of large and small velocity, was performed. It was shown that one dimensional systems exhibit a large variety of novel universality classes, contrary to systems in higher dimensions, where only one universality class is possible. The relation to Chirikov resonances, that are central in the theory of Chaos, was demonstrated. The general theory was applied and numerically tested for specific physically relevant examples.

cond-mat.stat-mech↗

arXiv2012

Transport in time-dependent random potentials

The classical dynamics in stationary potentials that are random both in space and time is studied. It can be intuitively understood with the help of Chirikov resonances that are central in the theory of Chaos, and explored quantitatively in the framework of the Fokker-Planck equation. In particular, a simple expression for the diffusion coefficient was obtained in terms of the average power density of the potential. The resulting anomalous diffusion in velocity is classified into universality classes. The general theory was applied and numerically tested for specific examples relevant for optics and atom optics.

cond-mat.stat-mech↗

arXiv2012

How coupled elementary units determine the dynamics of macroscopic glass-forming systems

We investigate the dynamics of a binary mixture Lennard-Jones system of different system sizes with respect to the importance of the properties of the underlying potential energy landscape (PEL). We show that the dynamics of small systems can be very well described within the continuous time random walk formalism, which is determined solely by PEL parameters. Finite size analysis shows that the diffusivity of large and small systems are very similar. This suggests that the PEL parameters of the small system also determine the local dynamics in large systems. The structural relaxation time, however, displays significant finite size effects. Furthermore, using a non-equilibrium configuration of a large system, we find that causal connections exist between close-by regions of the system. These findings can be described by the coupled landscape model for which a macroscopic system is described by a superposition of elementary systems each described by its PEL. A minimum coupling is introduced which accounts for the finite size behavior. The coupling strength, as the single adjustable parameter, becomes smaller closer to the glass transition.

cond-mat.stat-mech↗

arXiv2012

Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.

cond-mat.dis-nn↗

arXiv2013

Large deviations of cascade processes on graphs

Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical trajectories, which can be crucial for the understanding of the out-of-equilibrium phenomena, is still considered to be intractable in most cases. Here we introduce an efficient method to find and analyze optimized trajectories of cascade processes. We show that for a wide class of irreversible dynamical rules, this problem can be solved efficiently on large-scale systems.

cond-mat.stat-mech↗

arXiv2013

Enhanced tunneling conductivity induced by gelation of attractive colloids

We show that the formation of a gel by conducting colloidal particles leads to a dramatic enhancement in bulk conductivity, due to inter-particle electron tunneling, combining predictions from molecular dynamics simulations with structural measurements in an experimental colloid system. Our results show how colloidal gelation can be used as a general route to huge enhancements of conductivity, and suggest a feasible way for developing cheap materials with novel properties and low metal content.

cond-mat.soft↗

arXiv2013

Stiff directed lines in random media

We investigate the localization of stiff directed lines with bending energy by a short-range random potential. We apply perturbative arguments, Flory scaling arguments, a variational replica calculation, and functional renormalization to show that a stiff directed line in 1+d dimensions undergoes a localization transition with increasing disorder for d > 2=3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+1 dimensions and analyze the properties of the disorder dominated phase in detail. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1+d dimensions and of directed lines under tension in 1+3d dimensions, which is strongly supported by identical free energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation. We support the proposed relation to directed lines via multifractal analysis revealing an analogous Anderson transition-like scenario and a matching correlation length exponent. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

cond-mat.stat-mech↗

arXiv2013

Noise-Induced Synchronization, Desynchronization, and Clustering in Globally Coupled Nonidentical Oscillators

We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desychronize a system. By introducing noise in various ways, we find a novel estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone is sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desychronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise.

nlin.AO↗

arXiv2013

Integrability of zero-dimensional replica field theories at beta=1

Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica sigma models derived in the context of real symmetric random matrices. Specifically, the fermionic and the bosonic replica partition functions are proven to form a single (supersymmetric) Pfaff-KP hierarchy whose replica limit is shown to reproduce the celebrated nonperturbative formula for the density-density eigenvalue correlation function in the infinite-dimensional Gaussian Orthogonal Ensemble. Implications of the formalism outlined are briefly discussed.

math-ph↗

arXiv2013

Statistics of Avalanches with Relaxation, and Barkhausen Noise: A Solvable Model

We study a generalization of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model of a particle in a Brownian force landscape, including retardation effects. We show that under monotonous driving the particle moves forward at all times, as it does in absence of retardation (Middleton's theorem). This remarkable property allows us to develop an analytical treatment. The model with an exponentially decaying memory kernel is realized in Barkhausen experiments with eddy-current relaxation, and has previously been shown numerically to account for the experimentally observed asymmetry of Barkhausen-pulse shapes. We elucidate another qualitatively new feature: the breakup of each avalanche of the standard ABBM model into a cluster of sub-avalanches, sharply delimited for slow relaxation under quasi-static driving. These conditions are typical for earthquake dynamics. With relaxation and aftershock clustering, the present model includes important ingredients for an effective description of earthquakes. We analyze quantitatively the limits of slow and fast relaxation for stationary driving with velocity v>0. The v-dependent power-law exponent for small velocities, and the critical driving velocity at which the particle velocity never vanishes, are modified. We also analyze non-stationary avalanches following a step in the driving magnetic field. Analytically, we obtain the mean avalanche shape at fixed size, the duration distribution of the first sub-avalanche, and the time dependence of the mean velocity. We propose to study these observables in experiments, allowing to directly measure the shape of the memory kernel, and to trace eddy current relaxation in Barkhausen noise.

cond-mat.dis-nn↗