SEARCH · Searcharxiv

Results for “cond-mat.dis-nn”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 937 records · Page 52Linked to original sources

arXiv2018

Spectral properties of the trap model on sparse networks

One of the simplest models for the slow relaxation and aging of glasses is the trap model by Bouchaud and others, which represents a system as a point in configuration-space hopping between local energy minima. The time evolution depends on the transition rates and the network of allowed jumps between the minima. We consider the case of sparse configuration-space connectivity given by a random graph, and study the spectral properties of the resulting master operator. We develop a general approach using the cavity method that gives access to the density of states in large systems, as well as localisation properties of the eigenvectors, which are important for the dynamics. We illustrate how, for a system with sparse connectivity and finite temperature, the density of states and the average inverse participation ratio have attributes that arise from a non-trivial combination of the corresponding mean field (fully connected) and random walk (infinite temperature) limits. In particular, we find a range of eigenvalues for which the density of states is of mean-field form but localisation properties are not, and speculate that the corresponding eigenvectors may be concentrated on extensively many clusters of network sites.

cond-mat.dis-nn↗

arXiv2017

How to Suppress Dark States in Quantum Networks and Bio-Engineered Structures

Transport across quantum networks underlies many problems, from state transfer on a spin network to energy transport in photosynthetic complexes. However, networks can contain dark subspaces that block the transportation, and various methods used to enhance transfer on quantum networks can be viewed as equivalently avoiding, modifying, or destroying the dark subspace. Here, we exploit graph theoretical tools to identify the dark subspaces and show that asymptotically almost surely they do not exist for large networks, while for small ones they can be suppressed by properly perturbing the coupling rates between the network nodes. More specifically, we apply these results to describe the recently experimentally observed and robust transport behaviour of the electronic excitation travelling on a genetically-engineered light-harvesting cylinder (M13 virus) structure. We believe that these mainly topological tools may allow us to better infer which network structures and dynamics are more favourable to enhance transfer of energy and information towards novel quantum technologies.

quant-ph↗

arXiv2018

Topological phase transitions in random Kitaev $α$-chains

The topological phases of random Kitaev $α$-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↗

arXiv2018

Kac-Rice fixed point analysis for single- and multi-layered complex systems

We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac-Rice formalism, we show that the mean number of fixed points can be calculated as the expectation of the absolute value of the characteristic polynomial for a product of independent Gaussian (Ginibre) matrices. Furthermore, using techniques from Random Matrix Theory, we show that the high-dimensional limit of our system has a third-order phase transition between a phase with a single fixed point and a phase with exponentially many fixed points. This is result is universal in the sense that it does not depend on finer details of the correlations for the random maps.

math-ph↗

arXiv2018

Moments of the inverse participation ratio for the Laplacian on finite regular graphs

We investigate the first and second moments of the inverse participation ratio (IPR) for all eigenvectors of the Laplacian on finite random regular graphs with $n$ vertices and degree $z$. By exactly diagonalizing a large set of $z$-regular graphs, we find that as $n$ becomes large, the mean of the inverse participation ratio on each graph, when averaged over a large ensemble of graphs, approaches the numerical value $3$. This universal number is understood as the large-$n$ limit of the average of the quartic polynomial corresponding to the IPR over an appropriate $(n-2)$-dimensional hypersphere of $\mathbb{R}^n$. For a large, but not exhaustive ensemble of graphs, the mean variance of the inverse participation ratio for all graph Laplacian eigenvectors deviates from its continuous hypersphere average due to large graph-to-graph fluctuations that arise from the existence of highly localized modes.

math-ph↗

arXiv2018

The role of T-helper/T-suppressor ratio in the adaptive immune response: a dynamical model

Recent experimental studies have suggested the ratio between T-helper and T-suppressor lymphocytes as an index of immunosuppression in HIV, cancer, immunosenescence and inflammatory and auto-immune diseases. However, a quantitative understanding of the impact of this ratio on the immune response has lagged behind data and its validity as a tool for prognostic monitoring or therapeutic target remains an open question. In this work, we use statistical physics and dynamical systems approaches to analyze the time-dependent response to an antigen, of a simplified model of the adaptive immune system, which comprises B, T-helper and T-suppressor lymphocytes. The model is remarkably robust against changes in the noise level and kinetic parameters, but it is very sensitive to changes in the ratio between T-helper and T-suppressor lymphocytes, exhibiting, in particular, a transition from a responsive to an immuno-suppressed phase, as the ratio is lowered below a critical value, which is in line with experiments. This result supports the validity of the T-helper/T-suppressor ratio as an index of immunosuppression and may provide a useful theoretical benchmark to interpret and compare experiments.

q-bio.CB↗

arXiv2018

A Random Walk Perspective on Hide-and-Seek Games

We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of vertices of a random graph. Vertices at which items are hidden in the network are chosen at random as well, though with probabilities that may depend on degree. We pitch various hide and seek strategies against each other, and determine the efficiency of search strategies by computing the average number of hidden items that a searcher will uncover in a random walk of $n$ steps. Our analysis is based on the cavity method for finite single instances of the problem, and generalises previous work of De Bacco et al. [1] so as to cover degree-biased random walks. We also extend the analysis to deal with the thermodynamic limit of infinite system size. We study a broad spectrum of functional forms for the degree bias of both the hiding and the search strategy and investigate the efficiency of families of search strategies for cases where their functional form is either matched or unmatched to that of the hiding strategy. Our results are in excellent agreement with those of numerical simulations. We propose two simple approximations for predicting efficient search strategies. One is based on an equilibrium analysis of the random walk search strategy. While not exact, it produces correct orders of magnitude for parameters characterising optimal search strategies. The second exploits the existence of an effective drift in random walks on networks, and is expected to be efficient in systems with low concentration of small degree nodes.

physics.soc-ph↗

arXiv2019

Numerical study of barriers and valleys in the free-energy landscape of spin glasses

We study the problem of glassy relaxations in the presence of an external field in the highly controlled context of a spin-glass simulation. We consider a small spin glass in three dimensions (specifically, a lattice of size L=8, small enough to be equilibrated through a Parallel Tempering simulations at low temperatures, deep in the spin glass phase). After equilibrating the sample, an external field is switched on, and the subsequent dynamics is studied. The field turns out to reduce the relaxation time, but huge statistical fluctuations are found when different samples are compared. After taking care of these fluctuations we find that the expected linear regime is very narrow. Nevertheless, when regarded as a purely numerical method, we find that the external field is extremely effective in reducing the relaxation times.

cond-mat.dis-nn↗

arXiv2018

Noninteracting fermions in a trap and random matrix theory

We review recent advances in the theory of trapped fermions using techniques borrowed from random matrix theory (RMT) and, more generally, from the theory of determinantal point processes. In the presence of a trap, and in the limit of a large number of fermions $N \gg 1$, the spatial density exhibits an edge, beyond which it vanishes. While the spatial correlations far from the edge, i.e. close to the center of the trap, are well described by standard many-body techniques, such as the local density approximation (LDA), these methods fail to describe the fluctuations close to the edge of the Fermi gas, where the density is very small and the fluctuations are thus enhanced. It turns out that RMT and determinantal point processes offer a powerful toolbox to study these edge properties in great detail. Here we discuss the principal edge universality classes, that have been recently identified using these modern tools. In dimension $d=1$ and at zero temperature $T=0$, these universality classes are in one-to-one correspondence with the standard universality classes found in the classical unitary random matrix ensembles: soft edge (described by the "Airy kernel") and hard edge (described by the "Bessel kernel") universality classes. We further discuss extensions of these results to higher dimensions $d\geq 2$ and to finite temperature. Finally, we discuss correlations in the phase space, i.e., in the space of positions and momenta, characterized by the so called Wigner function.

cond-mat.stat-mech↗

arXiv2019

Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case

We consider the Langevin dynamics of a many-body system of interacting particles in $d$ dimensions, in a very general setting suitable to model several out-of-equilibrium situations, such as liquid and glass rheology, active self-propelled particles, and glassy aging dynamics. The pair interaction potential is generic, and can be chosen to model colloids, atomic liquids, and granular materials. In the limit ${d\to\infty}$, we show that the dynamics can be exactly reduced to a single one-dimensional effective stochastic equation, with an effective thermal bath described by kernels that have to be determined self-consistently. We present two complementary derivations, via a dynamical cavity method and via a path-integral approach. From the effective stochastic equation, one can compute dynamical observables such as pressure, shear stress, particle mean-square displacement, and the associated response function. As an application of our results, we derive dynamically the `state-following' equations that describe the response of a glass to quasistatic perturbations, thus bypassing the use of replicas. The article is written in a modular way, that allows the reader to skip the details of the derivations and focus on the physical setting and the main results.

cond-mat.dis-nn↗

arXiv2019

An experiment-oriented analysis of 2D spin-glass dynamics: a twelve time-decades scaling study

Recent high precision experimental results on spin-glass films ask for a detailed understanding of the domain-growth dynamics of two-dimensional spin glasses. To achieve this goal, we numerically simulate the out-equilibrium dynamics of the Ising spin glass for a time that spans close to twelve orders of magnitude (from picoseconds to order of a second), in systems large enough to avoid finite-size effects. We find that the time-growth of the size of the glassy domains is excellently described by a single scaling function. A single time-scale $τ(T)$ controls the dynamics. $τ(T)$ diverges upon approaching the $T=0$ critical point. The divergence of $τ(T\to 0)$ is Arrhenius-like, with a barrier height that depends very mildly on temperature. The growth of this barrier-height is best described by critical dynamics. As a side product we obtain an impressive confirmation of universality of the equilibrium behavior of two-dimensional spin-glasses.

cond-mat.dis-nn↗

arXiv2019

Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain

As an extension of the isotropic setting presented in the companion paper [J. Phys. A 52, 144002 (2019)], we consider the Langevin dynamics of a many-body system of pairwise interacting particles in $d$ dimensions, submitted to an external shear strain. We show that the anisotropy introduced by the shear strain can be simply addressed by moving into the co-shearing frame, leading to simple dynamical mean field equations in the limit ${d\to\infty}$. The dynamics is then controlled by a single one-dimensional effective stochastic process which depends on three distinct strain-dependent kernels - self-consistently determined by the process itself - encoding the effective restoring force, friction and noise terms due to the particle interactions. From there one can compute dynamical observables such as particle mean-square displacements and shear stress fluctuations, and eventually aim at providing an exact ${d \to \infty}$ benchmark for liquid and glass rheology. As an application of our results, we derive dynamically the 'state-following' equations that describe the static response of a glass to a finite shear strain until it yields.

cond-mat.dis-nn↗

arXiv2019

Compressed sensing reconstruction using Expectation Propagation

Many interesting problems in fields ranging from telecommunications to computational biology can be formalized in terms of large underdetermined systems of linear equations with additional constraints or regularizers. One of the most studied ones, the Compressed Sensing problem (CS), consists in finding the solution with the smallest number of non-zero components of a given system of linear equations $\boldsymbol y = \mathbf{F} \boldsymbol{w}$ for known measurement vector $\boldsymbol{y}$ and sensing matrix $\mathbf{F}$. Here, we will address the compressed sensing problem within a Bayesian inference framework where the sparsity constraint is remapped into a singular prior distribution (called Spike-and-Slab or Bernoulli-Gauss). Solution to the problem is attempted through the computation of marginal distributions via Expectation Propagation (EP), an iterative computational scheme originally developed in Statistical Physics. We will show that this strategy is comparatively more accurate than the alternatives in solving instances of CS generated from statistically correlated measurement matrices. For computational strategies based on the Bayesian framework such as variants of Belief Propagation, this is to be expected, as they implicitly rely on the hypothesis of statistical independence among the entries of the sensing matrix. Perhaps surprisingly, the method outperforms uniformly also all the other state-of-the-art methods in our tests.

stat.ML↗

arXiv2022

Exact percolation probabilities for a square lattice: Site percolation on a plane, cylinder, and torus

We have found analytical expressions (polynomials) of the percolation probability for site percolation on a square lattice of size $L \times L$ sites when considering a plane (the crossing probability in a given direction), a cylinder (spanning probability), and a torus (wrapping probability along one direction). Since some polynomials are extremely cumbersome, they are presented as separate files in Supplemental material. The system sizes for which this was feasible varied up to $L=17$ for a plane, up to $L=16$ for a cylinder, and up to $L=12$ for a torus. To obtain a percolation probability polynomial, all possible combinations of occupied and empty sites have to be taken into account. However, using dynamic programming along with some ideas related to the topology, we offer an algorithm which allows a significant reduction in the number of configurations requiring consideration. A rigorous formal description of the algorithm is presented. Divisibility properties of the polynomials have been rigorously proved. Reliability of the polynomials obtained have been confirmed by the divisibility tests. The wrapping probability polynomials on a torus provide a better estimate of the percolation threshold than that from the spanning probability polynomials. Surprisingly, even a naive finite size scaling analysis allows an estimate to be obtained of the percolation threshold $p_c = 0.59269$.

cond-mat.stat-mech↗

arXiv2019

Variational approach to unsupervised learning

Deep belief networks are used extensively for unsupervised stochastic learning on large datasets. Compared to other deep learning approaches their layer-by-layer learning makes them highly scalable. Unfortunately, the principles by which they achieve efficient learning are not well understood. Numerous attempts have been made to explain their efficiency and applicability to a wide class of learning problems in terms of principles drawn from cognitive psychology, statistics, information theory, and more recently physics, but quite often these imported principles lack strong scientific foundation. Here we demonstrate how one can arrive at convolutional deep belief networks as potential solution to unsupervised learning problems without making assumptions about the underlying framework. To do this, we exploit the notion of symmetry that is fundamental in machine learning, physics and other fields, utilizing the particular form of the functional renormalization group in physics.

cond-mat.dis-nn↗

arXiv2019

Anderson localization induced by complex potential

Uncorrelated disorder potential in one-dimensional lattice definitely induces Anderson localization, while quasiperiodic potential can lead to both localized and extended phases, depending on the potential strength. We investigate the Anderson localization in one-dimensional lattice with nonHermitian complex disorder and quasiperiodic potential. We present a non-Hermitian SSH chain to demonstrate that a nonzero imaginary disorder on-site potential can induce the standard Anderson localization. We also show that the non-Hermitian Aubry-Andre (AA) model exhibits a transition in parameter space, which separates the localization and delocalization phases and is determined by the self-duality of the model. It indicates that a pure imaginary quasiperiodic potential takes the same role as a real quasiperiodic potential in the transition point between localization and delocalization. Remarkably, a system with complex quasiperiodic potential exhibits interference-like pattern on the transition points.

cond-mat.dis-nn↗

arXiv2019

Singular Spectrum and Recent Results on Hierarchical Operators

We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical operators and matrices. We proceed to contrast the localizing effect of the hierarchical structure in the deterministic setting with previous results and conjectures in the random setting. Furthermore, we survey stronger localization statements truly exploiting the disorder for the hierarchical Anderson model and report recent results concerning the spectral statistics of the ultrametric random matrix ensemble.

math-ph↗

arXiv2018

Effects of Time Horizons on Influence Maximization in the Voter Dynamics

In this paper we analyze influence maximization in the voter model with an active strategic and a passive influencing party in non-stationary settings. We thus explore the dependence of optimal influence allocation on the time horizons of the strategic influencer. We find that on undirected heterogeneous networks, for short time horizons, influence is maximized when targeting low-degree nodes, while for long time horizons influence maximization is achieved when controlling hub nodes. Furthermore, we show that for short and intermediate time scales influence maximization can exploit knowledge of (transient) opinion configurations. More in detail, we find two rules. First, nodes with states differing from the strategic influencer's goal should be targeted. Second, if only few nodes are initially aligned with the strategic influencer, nodes subject to opposing influence should be avoided, but when many nodes are aligned, an optimal influencer should shadow opposing influence.

physics.soc-ph↗