# Physics - Disordered Systems and Neural Networks Publications (50)

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## Physics - Disordered Systems and Neural Networks Publications

We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values. Additionally, in this model variant all edges are directed. Read More

The interplay between quantum fluctuations and disorder is investigated in a spin-glass model, in the presence of a uniform transverse field $\Gamma$, and a longitudinal random field following a Gaussian distribution with width $\Delta$. The model is studied through the replica formalism. This study is motivated by experimental investigations on the LiHo$_x$Y$_{1-x}$F$_4$ compound, where the application of a transverse magnetic field yields rather intriguing effects, particularly related to the behavior of the nonlinear magnetic susceptibility $\chi_3$, which have led to a considerable experimental and theoretical debate. Read More

The mean-field theory for disordered electron systems without interaction is widely and successfully used to describe equilibrium properties of materials over the whole range of disorder strengths. However, it fails to take into account the effects of quantum coherence and information of localization. Vertex corrections due to multiple back-scatterings may drive the electrical conductivity to zero and make expansions around the mean field in strong disorder problematic. Read More

We present a first-principles-based many-body typical medium dynamical cluster approximation TMDCA@DFT method for characterizing electron localization in disordered structures. This method applied to monolayer hexagonal boron nitride shows that the presence of a boron vacancies could turn this wide-gap insulator into a correlated metal. Depending on the strength of the electron interactions, these calculations suggest that conduction could be obtained at a boron vacancy concentration as low as $1. Read More

We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. Read More

We study the influence of the electron-magnon interaction on the particle transport in strongly disordered systems. The analysis is based on results obtained for a single hole in the one-dimensional t-J model. Unless there exists a mechanism that localizes spin excitations, the charge carrier remains delocalized even for a very strong disorder and shows subdiffusive motion up to the longest accessible times. Read More

We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a 'non-Fermi liquid' phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $\epsilon$-expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. Read More

We propose theoretical approach based on combination of graph theory and generalized Ising model (GIM), which enables systematic determination of extremal structures for crystalline solids without any information about interactions or constituent elements. The conventional approach to find such set of structure typically employs configurational polyhedra (CP) on configuration space based on GIM description, whose vertices can always be candidates to exhibit maximum or minimum physical quantities. We demonstrate that the present approach can construct extended CP whose vertices not only include those found in conventional CP, but also include other topologically and/or configurationally characteristic structures on the same dimensional configuration space with the same set of figures composed of underlying lattice points, which therefore has significant advantage over the conventional approach. Read More

The resilience and fragility of real complex connected systems can be understood through their abrupt behaviors of functioning percolating node clusters against external perturbations based on a random or designed scheme. For the models of the phenomena of the discontinuous transitions against random damages, previous studies focus on the introduction of new dependency or interaction among nodes to generate a more aggressive network breakdown process in the case of networks with undirected interactions or the coupling between layers with different types of interactions to bring about cascading failures in the case of multiplex networks. Yet for many systems whose representation is easily enough as networks with directed interactions, a model of structural resilience with a concisely defined procedure and also an explicit analytical framework is still lacking. Read More

Spin-3/2 topological superconductors (TSCs) may be realized in ultracold atoms or doped semimetals. We consider a p-wave model with linear and cubic dispersing Majorana surface bands. We show that the latter are unstable to interactions, which generate a spontaneous thermal quantum Hall effect (TQHE). Read More

We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. The coupling to the central site partially dilutes the Anderson localized peak towards the nearly resonant sites. In particular, the number of resonantly coupled sites remains finite in the thermodynamic limit. Read More

We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional traps across the thermal crossover from an amorphous solid- to liquid-like behaviors. While static correlations, that investigate the translational and bond orientational order in the confinements, show the footprints of hexatic-like phase at low temperature, dynamics of the particles slow down considerably in this state -- reminiscent of a supercooled liquid. Using density correlations, we probe intriguing signatures of long-lived inhomogeneities due to the interplay of the irregularity in the confinement and long-range Coulomb interactions. Read More

Following numerous earlier studies, extensive simulations and analyses were made on the continuous interaction distribution Gaussian model and the discrete bimodal interaction distribution Ising Spin Glass (ISG) models in dimension two (P.H. Lundow and I. Read More

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. Read More

In the social, behavioral, and economic sciences, it is an important problem to predict which individual opinions will eventually dominate in a large population, if there will be a consensus, and how long it takes a consensus to form. This idea has been studied heavily both in physics and in other disciplines, and the answer depends strongly on both the model for opinions and for the network structure on which the opinions evolve. One model that was created to study consensus formation quantitatively is the Deffuant model, in which the opinion distribution of a population evolves via sequential random pairwise encounters. Read More

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. Read More

We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical attractors to recognize and reconstruct partially corrupted patterns. Traditional parameters of pattern recognition theory, such as sparsity, fidelity, and capacity are related to physical parameters, such as nucleation barriers, interaction range, and non-equilibrium assembly forces. Read More

We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading to global coherent oscillations in the network. This scenario may be relevant to action potential generation in certain sensory neurons, which possess myelinated distal dendritic tree-like arbors with excitable nodes of Ranvier at peripheral and branching nodes and exhibit noisy periodic sequences of action potentials. Read More

Functionals of a stochastic process Y(t) model many physical time-extensive observables, e.g. particle positions, local and occupation times or accumulated mechanical work. Read More

We propose a new framework to understand how quantum effects may impact on the dynamics of neural networks. We implement the dynamics of neural networks in terms of Markovian open quantum systems, which allows us to treat thermal and quantum coherent effects on the same footing. In particular, we propose an open quantum generalisation of the celebrated Hopfield neural network, the simplest toy model of associative memory. Read More

The control of brain dynamics provides great promise for the enhancement of cognitive function in humans, and by extension the betterment of their quality of life. Yet, successfully controlling dynamics in neural systems is particularly challenging, not least due to the immense complexity of the brain and the large set of interactions that can affect any single change. While we have gained some understanding of the control of single neurons, the control of large-scale neural systems---networks of multiply interacting components---remains poorly understood. Read More

We numerically investigate the statistical properties of electrochemical capacitance in disordered two-dimensional mesoscopic capacitors. Based on the tight-binding Hamiltonian, the Green's function formalism is adopted to study the average electrochemical capacitance, its fluctuation as well as the distribution of capacitance of the disordered mesoscopic capacitors for three different ensembles: orthogonal (symmetry index \beta=1), unitary (\beta=2), and symplectic (\beta=4). It is found that the electrochemical capacitance in the disordered systems exhibits universal behavior. Read More

We demonstrate that the normalised localization length $\beta$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $\beta=x^*/(1+x^*)$. The scaling parameter of the model is defined as $x^*\propto(b_{eff}^2/N)^\delta$, where $b_{eff}$ is the average number of non-zero elements per matrix row, $N$ is the matrix size, and $\delta\sim 1$. Additionally, we show that $x^*$ also scales the spectral properties of the model (up to certain sparsity) characterized by the spacing distribution of eigenvalues. Read More

Time periodic driving serves not only as a convenient way to engineer effective Hamiltonians, but also as a means to produce intrinsically dynamical phases that do not exist in the static limit. A recent example of the latter are 2D chiral Floquet (CF) phases exhibiting anomalous edge dynamics that pump discrete packets of quantum information along one direction. In non-fractionalized systems with only bosonic excitations, this pumping is quantified by a dynamical topological index that is a rational number -- highlighting its difference from the integer valued invariant underlying equilibrium chiral phases (e. Read More

We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any second derivatives. The underlying idea is to use two nearby points in configuration space to locate the path of slowest ascent. Read More

We study the spatial fluctuations of the Casimir-Polder force experienced by an atom or a small sphere moved above a metallic plate at fixed separation distance. We discover that unlike the mean force, the magnitude of these fluctuations dramatically depends on the relaxation of conduction electron in the bulk, achieving values that differ by orders of magnitude depending on whether the dissipative Drude and dissipationless plasma prescriptions are used for the metal. We also show that fluctuations suffer a spectacular decrease at large distances in the case of non null temperature. Read More

**Authors:**B. Li, Y. Kawakita, Q. Zhang, H. Wang, M. Feygenson, H. L. Yu, D. Wu, K. Ohara, T. Kikuchi, K. Shibata, T. Yamada, Y. Chen, J. Q. He, D. Vaknin, R. Q. Wu, K. Nakajima, M. G. Kanatzidis

A solid conducts heat through both transverse and longitudinal acoustic phonons, but a liquid employs only longitudinal vibrations. Here, we report that the crystalline solid AgCrSe2 has liquid-like thermal conduction. In this compound, Ag atoms exhibit a dynamic duality that they are exclusively involved in intense low-lying transverse acoustic phonons while they also undergo local fluctuations inherent in an order-to-disorder transition occurring at 450 K. Read More

Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterwards exhibiting a steady state with a constant mean stress. In stress controlled experiments the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Read More

Quantum phase transitions of disordered three-dimensional (3D) Weyl semimetals (WSMs) are investigated through quantum conductance calculations and finite-size scaling of localization length. Contrary to a previous belief that a direct transition from a WSM to a diffusive metal (DM) occurs, an intermediate phase of Chern insulator (CI) between the two distinct metallic phases should exist. The critical exponent of localization length is $\nu\simeq 1. Read More

We employ Random Matrix Theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength $\gamma_{\rm CPA}$ and energy $E_{\rm CPA}$, for which a CPA occurs are expressed in terms of the eigenmodes of the isolated cavity -- thus carrying over the information about the chaotic nature of the target -- and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities. Read More

We theoretically study the single particle Green function of a three dimensional disordered Weyl semimetal using a combination of techniques. These include analytic T-matrix and renormalization group methods with complementary regimes of validity, and an exact numerical approach based on the kernel polynomial technique. We show that at any nonzero disorder, Weyl excitations are not ballistic: they instead have a nonzero linewidth that for weak short-range disorder arises from non-perturbative resonant impurity scattering. Read More

A characteristic property of networks is their ability to propagate influences, such as infectious diseases, behavioral changes, and failures. An especially important class of such contagious dynamics is that of cascading processes. These processes include, for example, cascading failures in infrastructure systems, extinctions cascades in ecological networks, and information cascades in social systems. Read More

We analyze the ground state localization properties of an array of identical interacting spinless fermionic chains with quasi-random disorder, using non-perturbative Renormalization Group methods. In the single or two chains case localization persists while for a larger number of chains a different qualitative behavior is generically expected, unless the many body interaction is vanishing. This is due to number theoretical properties of the frequency, similar to the ones assumed in KAM theory, and cancellations due to Pauli principle which in the single or two chains case imply that all the effective interactions are irrelevant; in contrast for a larger number of chains relevant effective interactions are present. Read More

Simultaneous recordings from N electrodes generate N-dimensional time series that call for efficient representations to expose relevant aspects of the underlying dynamics. Binning the time series defines neural activity vectors that populate the N-dimensional space as a density distribution, especially informative when the neural dynamics performs a noisy path through metastable states (often a case of interest in neuroscience); this makes clustering in the N-dimensional space a natural choice. We apply a variant of the 'mean-shift' algorithm to perform such clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are uncorrelated from memory attractors. Read More

Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the search for material systems to realize such phases have been strongly influenced by this. Here we theoretically demonstrate topological insulators in systems with a random distribution of sites in space, i. e. Read More

We analyze many body localization (MBL) in an interacting quasi-periodic system in one-dimension. We explore effects of nearest-neighbour repulsion on a system of spin-less fermions in which below a threshold value of quasi-periodic potential $h < h_c$, the system has single particle mobility edge at $\pm E_c$ while for $ h > h_c$ all the single particle states are localized. We demonstrate based on our numerical calculation of participation ratio in the Fock space and Shannon entropy, that both for $h < h_c$ and $h > h_c$, the interacting system can have many-body mobility edge. Read More

It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry breaking glass solution in the case of non-reflective symmetry diagonal operators used instead of Ising spins. As an example, axial quadrupole moments in place of Ising spins are considered and the boundary value $p_{c_{1}}\cong 2.5$ is found. Read More

Conventional wisdom tells us that the Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states in a class of systems in which the Hilbert space can be partitioned in a way that the disorder affects only certain subspaces causing localization, while the states in the other subspaces remain extended. The coexistence of localized and extended states is achieved when the states in both types of subspaces overlap spatially and spectrally. Read More

Glass-to-glass and liquid-to-liquid phase transitions were observed many years ago in bulk and confined water with or without applied pressure. It is shown that they result from the competition of two-liquid phases separated by an enthalpy difference depending on temperature. The model is based on the classical nucleation equation of these phases completed by this enthalpy saving existing at all temperatures and a pressure contribution. Read More

Advances in experimental techniques are generating an increasing volume of publicly available ecologically and biologically relevant data and are revealing that living systems are characterized by the emergence of recurrent patterns and regularities. Several studies indicate that metabolic, gene-regulatory and species interaction networks possess a non-random architecture. One of the observed emergent patterns is sparsity, i. Read More

The asymptotical behavior of physical quantities, like the order parameter, the replicon and longitudinal masses, is studied around the zero-field spin glass transition point when a small external magnetic field is applied. An effective field theory to model this asymptotics contains a small perturbation in its Lagrangian which breaks the zero-field symmetry. A first order renormalization group supplemented by perturbational results provides the scaling functions. Read More

A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to considerably simplify the proofs. The solutions of the quenched diluted case and the random monomer case are explained. Read More

Crack nucleation is a ubiquitous phenomena during materials failure, because stress focuses on crack tips. It is known that exceptions to this general rule arise in the limit of strong disorder or vanishing mechanical stability, where stress distributes over a divergent length scale and the material displays diffusive damage. Here we show, using simulations, that a class of diluted lattices displays a new critical phase when they are below isostaticity, where stress never concentrates, damage always occurs over a divergent length scale, and catastrophic failure is avoided. Read More

Covariance matrices are fundamental to the analysis and forecast of economic, physical and biological systems. Although the eigenvalues $\{\lambda_i\}$ and eigenvectors $\{\bf{u}_i\}$ of a covariance matrix are central to such endeavors, in practice one must inevitably approximate the covariance matrix based on data with finite sample size $n$ to obtain empirical eigenvalues $\{\tilde{\lambda}_i\}$ and eigenvectors $\{\tilde{\bf{u}}_i\}$, and therefore understanding the error so introduced is of central importance. We analyze eigenvector error $\|\bf{u}_i - \tilde{\bf{u}}_i \|^2$ while leveraging the assumption that the true covariance matrix is drawn from an ensemble with known spectral properties, such as the distribution of and the gaps between eigenvalues. Read More

Fisher's geometric model was originally introduced to argue that complex adaptations must occur in small steps because of pleiotropic constraints. When supplemented with the assumption of additivity of mutational effects on phenotypic traits, it provides a simple mechanism for the emergence of genotypic epistasis from the nonlinear mapping of phenotypes to fitness. Of particular interest is the occurrence of sign epistasis, which is a necessary condition for multipeaked genotypic fitness landscapes. Read More

Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order parameters. Read More

Obtaining the exact multi-time correlations for one-dimensional growth models
described by the Kardar-Parisi-Zhang (KPZ) universality class is presently an
outstanding open problem. Here, we study the joint probability distribution
function (JPDF) of the height of the KPZ equation with droplet initial
conditions, at two different times $t_1

We comment on an expression for positive sound dispersion (PSD) in fluids and analysis of PSD from molecular dynamics simulations reported in the Letter by Fomin et al (J.Phys.:Condens. Read More

The computational complexity conjecture of NP $\nsubseteq$ BQP implies that there should be an exponentially small energy gap for Quantum Annealing (QA) of NP-hard problems. We aim to verify how this computation originated gapless point could be understood based on physics, using the quantum Monte Carlo method. As a result, we found a phase transition detectable only by the divergence of fidelity susceptibility. Read More

At low temperatures the dynamical degrees of freedom in amorphous solids are tunnelling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a "TLS-glass", described by the random field Ising model with random $1/r^3$ interactions. In this paper we perform a self consistent mean field calculation, previously used to study the electron-glass (EG) model [A. Read More