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

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## Physics - Disordered Systems and Neural Networks Publications

A novel approach to predict the atomic densities of amorphous materials is explored on the basis of Car-Parrinello molecular dynamics (CPMD) in density functional theory. Despite that determination of the atomic density of matter is crucial in understanding its physical properties, no such method has ever been proposed for amorphous materials until now. The key process in our approach is that we generate multiple amorphous structures with several different volumes by CPMD simulations and average the total energies at each volume. Read More

The Green's function contains much information about physical systems. Mathematically, the fractional moment method (FMM) developed by Aizenman and Molchanov connects the Green's function and the transport of electrons in the Anderson model. Recently, it has been discovered that the Green's function on a graph can be represented using self-avoiding walks on a graph, which allows us to connect localization properties in the system and graph properties. Read More

We complete the analysis of the phase diagram of the complex branching Brownian motion energy model by studying Phases I, III and boundaries between all three phases (I-III) of this model. For the properly rescaled partition function, in Phase III and on the boundaries I/III and II/III, we prove a central limit theorem with a random variance. In Phase I and on the boundary I/II, we prove an a. Read More

The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free", indicating some type of criticality. In spite of attempts to invoke "Self-Organized Criticality", the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Read More

This paper outlines a methodological approach to generate adaptive agents driving themselves near points of criticality. Using a synthetic approach we construct a conceptual model that, instead of specifying mechanistic requirements to generate criticality, exploits the maintenance of an organizational structure capable of reproducing critical behavior. Our approach captures the well-known principle of universality that classifies critical phenomena inside a few universality classes of systems without relying on specific mechanisms or topologies. Read More

We unveil a novel and unexpected manifestation of Anderson localization of matter wave packets that carry a finite average velocity: after an initial ballistic motion, the packet center-of-mass experiences a retroreflection and slowly returns to its initial position. We describe this effect both numerically and analytically in dimension 1, and show that it is destroyed by weak particle interactions which act as a decoherence process. The retroreflection is also present in higher dimensions, provided the dynamics is Anderson localized. Read More

This comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power law interactions, $r^{-\alpha}$, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has been earlier argued [1, 2] that this model obeys the dimensional constraint suggesting the delocalization of all finite temperature states in thermodynamic limit for $\alpha \leq 2d$ in a $d$-dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model in Ref. Read More

We introduce a new type of states for light in multimode waveguides featuring strongly enhanced or reduced spectral correlations. Based on the experimentally measured multi-spectral transmission matrix of a multimode fiber, we generate a set of states that outperform the established "principal modes" in terms of the spectral stability of their output spatial field profiles. Inverting this concept also allows us to create states with a minimal spectral correlation width, whose output profiles are considerably more sensitive to a frequency change than typical input wavefronts. Read More

We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power law tails with continuously varying non-universal powers. Read More

We study Harmonic Soft Spheres as a model of thermal structural glasses in the limit of infinite dimensions. We show that cooling, compressing and shearing a glass lead to a Gardner transition and, hence, to a marginally stable amorphous solid as found for Hard Spheres systems. A general outcome of our results is that a reduced stability of the glass favors the appearance of the Gardner transition. Read More

We theoretically study a one-dimensional (1D) mutually incommensurate bichromatic lattice system which has been implemented in ultracold atoms to study quantum localization. It has been universally believed that the tight-binding version of this bichromatic incommensurate system is represented by the well-known Aubry-Andre model. Here we establish that this belief is incorrect and that the Aubry-Andre model description, which applies only in the extreme tight-binding limit of very deep primary lattice potential, generically breaks down near the localization transition due to the unavoidable appearance of single-particle mobility edges (SPME). Read More

We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits generated by a time-dependent spin-1/2 XY Hamiltonian, we give an analytic formula for the Lieb-Robinson bounded commutator norm of a local observable, and show that it can be efficiently evaluated by a classical computer even when the explicit Heisenberg time evolution cannot. Because this quantity bounds the average error incurred by truncating the evolution to a spatially limited region, we demonstrate dynamical localization as a mechanism for classically simulating quantum computation, using examples of localized phases under certain spatio-temporal disordered Hamiltonians. Read More

Consider random linear estimation with Gaussian measurement matrices and noise. One can compute infinitesimal variations of the mutual information under infinitesimal variations of the signal-to-noise ratio or of the measurement rate. We discuss how each variation is related to the minimum mean-square error and deduce that the two variations are directly connected through a very simple identity. Read More

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals -- the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. Read More

The critical behavior of the random field $O(N)$ model driven at a uniform velocity is investigated at zero-temperature. From naive phenomenological arguments, we introduce a dimensional reduction property, which relates the large-scale behavior of the $D$-dimensional driven random field $O(N)$ model to that of the $(D-1)$-dimensional pure $O(N)$ model. This is an analogue of the dimensional reduction property in equilibrium cases, which states that the large-scale behavior of $D$-dimensional random field models is identical to that of $(D-2)$-dimensional pure models. Read More

The rich-club concept has been introduced in order to characterize the presence of a cohort of nodes with a large number of links (rich nodes) that tend to be well connected between each other, creating a tight group (club). Rich-clubness defines the extent to which a network displays a topological organization characterized by the presence of a node rich-club. It is crucial for the investigation of internal organization and function of networks arising in systems of disparate fields such as transportation, social, communication and neuroscience. Read More

In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down completely, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge both for experiments and theory. Here, we experimentally explore the relaxation dynamics of an interacting gas of fermionic potassium atoms loaded in a two-dimensional optical lattice with different quasi-periodic potentials along the two directions. Read More

Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible neurons and another layer of hidden binary neurons, so it could serve as the building block for a multilayered deep-learning system. We then demonstrate that the Hopfield network can learn to form a faithful internal representation of the observed samples, with the learned memory patterns being prototypes of the input data. Read More

Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics like an effective inertia. In biological neuron networks this inertia is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of inertia affect the network dynamics is an open issue not yet addressed due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Read More

We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel libraries such as PETSc/SLEPc combined with high-performance computing approaches in order to overcome the large memory requirements to be able to study systems whose Hilbert space dimension comprises over 9 billion independent quantum states. Moreover, we provide descriptions on the parallel approach used for the three most important stages of the simulation: handling the Hilbert subspace basis, constructing a matrix representation for a generic Hamiltonian operator and the time evolution of the system by means of the Krylov subspace methods. Read More

**Authors:**P. W. Hess, P. Becker, H. B. Kaplan, A. Kyprianidis, A. C. Lee, B. Neyenhuis, G. Pagano, P. Richerme, C. Senko, J. Smith, W. L. Tan, J. Zhang, C. Monroe

Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatiotemporal resolution, decoupling from the external environment, and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. Read More

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter $K_c$ takes its universal Giamarchi-Schulz value $K_{c}=3/2$. Read More

We propose a generalized Langevin formalism to describe transport in combs and similar ramified structures. Our approach consists of a Langevin equation without drift for the motion along the backbone. The motion along the secondary branches may be described either by a Langevin equation or by other types of random processes. Read More

We show the localization phase transition and its effect on three dynamical processes for an extended Aubry-Andr\'e-Harper model with incommensurate on-site and hopping potentials. With the extended Aubry-Andr\'e-Harper model, we illustrate the localization transition of all eigenstates and fractal characters of the eigenenergy band versus system parameter. To examine the effect of localization transition to dynamical process, an adiabatic pumping of the edge states are examined. Read More

Two topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC was shown to equal a moment of a summed quasiprobability. Read More

We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labelled entanglement spectra pertaining to the fully localized and fully thermal regimes. Read More

We study the slow stochastic dynamics near the depinning threshold of an elastic interface in a random medium by solving a particularly suited model of hopping interacting particles which belongs to the quenched-Edwards-Wilkinson depinning universality class. The model allows us to compare the cases of uniformly activated and Arrhenius activated hops. In the former case, the velocity accurately follows a standard scaling law of the force and noise intensity with the analog of the thermal rounding exponent satisfying a modified "hyperscaling" relation. Read More

We consider the statistical properties of interaction parameter estimates obtained by the direct coupling analysis (DCA) approach to learning interactions from large data sets. Assuming that the data are generated from a random background distribution, we determine the distribution of inferred interactions. Two inference methods are considered: the L2 regularized naive mean-field inference procedure (regularized least squares, RLS), and the pseudo-likelihood maximization (plmDCA). Read More

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. Read More

The relationship between the spectral density and free energy of a spin system is considered. The analytical expressions allowing for the calculation of the spectral density for solvable models are determined. A linear Ising model is taken for testing the approach. Read More

We study glass transitions and jamming of supercooled vectorial spin systems without quenched disorder in a large dimensional limit. Our theory provides a unified mean-field theoretical framework for glass transitions of rotational degree of freedoms such as color angles in the continuous coloring of graphs, vector spins of geometrically frustrated magnets, directors of Janus particles and ellipsoids. The rotational glass transitions accompany various types of replica symmetry breaking. Read More

Assessing whether a given network is typical or atypical for a random-network ensemble (i.e., network-ensemble comparison) has widespread applications ranging from null-model selection and hypothesis testing to clustering and classifying networks. Read More

Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and computer science. In a path-breaking paper based on the non-rigorous `cavity method', physicists predicted not only the existence of a replica symmetry breaking phase transition in such models but also sketched a detailed picture of the evolution of the Gibbs measure within the replica symmetric phase and its impact on important problems in combinatorics, computer science and physics [Krzakala et al. Read More

The chiral anomaly in Weyl semimetals states that the left- and right-handed Weyl fermions, constituting the low energy description, are not individually conserved, resulting, for example, in a negative magnetoresistance in such materials. Recent experiments see strong indications of such an anomalous resistance response; however, with a response that at strong fields is more sharply peaked for parallel magnetic and electric fields than expected from simple theoretical considerations. Here, we uncover a mechanism, arising from the interplay between the angle-dependent Landau level structure and long-range scalar disorder, that has the same phenomenology. Read More

The evolution of cooperation in situations where selfish behavior would lead to defection is at the root of the formation of human societies and has attracted a lot of attention as a result. In structured populations, both spatial clustering of cooperators in lattice-like topologies, as well as heterogeneous contact networks, have been shown to favor cooperation in social dilemmas. Here, we present a unified framework that can describe and quantify the formation of spatial clusters of cooperators in a metric space, and also represent heterogeneous contact networks, in particular scale-free topologies as observed in most real networks. Read More

Many-body localization has become an important phenomenon for illuminating a potential rift between non-equilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent $\nu \ge 2$ in one dimensional systems. Read More

We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency spectrum as sharp, distinct peaks, a feature often found in real-world networks. Read More

A model for describing a growing length-scale near the glass transition point is introduced. We assume that, in a subsystem whose density is above a certain threshold value, $\rho_{\rm c}$, owing to topological restrictions, particle rearrangements are highly suppressed (i.e. Read More

One of the most powerful findings of statistical physics is the discovery of universality classes which can be used to categorize and predict the behavior of seemingly different systems. However, many real--world complex networks have not been fitted to the existing universality classes. Here, we study a realistic spatial network model with link-lengths of a characteristic scale $\zeta$. Read More

The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground state subspace of a certain quantum optimization problem. This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful. Read More

Using analytical arguments and computer simulations we show that the dependence of the hopping carrier mobility on the electric field $\mu(F)/\mu(0)$ in a system of random sites is determined by the localization length $\alpha$ and not by the concentration of sites $N$. This result is in drastic contrast to what is usually assumed in the literature for theoretical description of experimental data and for device modeling, where $N^{-1/3}$ is considered as the decisive length scale for $\mu(F)$. We show that although the limiting value $\mu(F \rightarrow 0)$ is determined by the ratio $N^{-1/3}/\alpha$, the dependence $\mu(F)/\mu(0)$ is sensitive to the magnitude of $\alpha$ and not to $N^{-1/3}$. Read More

In most semiconductors and insulators the presence of a small density of charged impurities cannot be avoided, but their effect can be reduced by compensation doping, i.e. by introducing defects of opposite charge. Read More

We calculate the level compressibility $\chi(W,L)$ of the energy levels inside $[-L/2,L/2]$ for the Anderson model on infinitely large random regular graphs with on-site potentials distributed uniformly in $[-W/2,W/2]$. We show that $\chi(W,L)$ approaches the limit $\lim_{L \rightarrow 0^+} \chi(W,L) = 0$ for a broad interval of the disorder strength $W$ within the extended phase, including the region of $W$ close to the critical point for the Anderson transition. These results strongly suggest that the energy levels follow the Wigner-Dyson statistics in the extended phase, which implies on the absence of non-ergodic extended wavefunctions. Read More

In previously identified forms of remote synchronization between two nodes, the intermediate portion of the network connecting the two nodes is not synchronized with them but generally exhibits some coherent dynamics. Here we report on a network phenomenon we call incoherence-mediated remote synchronization (IMRS), in which two non-contiguous parts of the network are identically synchronized while the dynamics of the intermediate part is statistically and information-theoretically incoherent. We identify mirror symmetry in the network structure as a mechanism allowing for such behavior, and show that IMRS is robust against dynamical noise as well as against parameter changes. Read More

We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed. Read More

We study quantum spin systems with quenched Gaussian disorder. We prove that the variance of all physical quantities in a certain class vanishes in the infinite volume limit. We study also replica symmetry breaking phenomena, where the variance of an overlap operator in the other class does not vanish in the replica symmetric Gibbs state. Read More

The largest eigenvalue of a network's adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expression relating the value of the largest eigenvalue of any network to the largest eigenvalue of two network subgraphs, considered as isolated: The hub with its immediate neighbors and the densely connected set of nodes with maximum $K$-core index. We validate this formula showing that it predicts with good accuracy the largest eigenvalue of a large set of synthetic and real-world topologies, with no exception. Read More

Liquid-liquid transition (LLT) in single-component liquids is one of the most mysterious phenomena in condensed matter. So far this problem has attracted attention mainly from the purely scientific viewpoint. Here we report the first experimental study on an impact of surface nano-structuring on LLT by using a surface treatment called rubbing, which is the key technology for the production of liquid crystal displays. Read More

We present analytical results for the distribution of first hitting times of random walkers (RWs) on directed Erd\H{o}s-R\'enyi (ER) networks. Starting from a random initial node, a random walker hops randomly along directed edges between adjacent nodes in the network. The path terminates either by the retracing scenario, when the walker enters a node which it has already visited before, or by the trapping scenario, when it becomes trapped in a dead-end node from which it cannot exit. Read More

We theoretically study the conductivity in arrays of metallic grains due to the variable-range multiple cotunneling of electrons with short-range (screened) Coulomb interaction. The system is supposed to be coupled to random stray charges in the dielectric matrix that are only loosely bounded to their spatial positions by elastic forces. The flexibility of the stray charges gives rise to a polaronic effect, which leads to the onset of Arrhenius-like conductivity behavior at low temperatures, replacing conventional Mott variable-range hopping. Read More