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

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## Physics - Disordered Systems and Neural Networks Publications

**Authors:**Haiping Huang

Synapses in real neural circuits can take discrete values, including zero (silent or potential) synapses. The computational role of zero synapses in unsupervised feature learning of unlabeled noisy data is still unclear, yet important to understand how the sparseness of synaptic activity is shaped during learning and its relationship with receptive field formation. Here, we formulate this kind of sparse feature learning by statistical mechanics approach. Read More

Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. Read More

The main goal of the paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate a decomposition procedure for the conditional probability function of sequences considered as the high-order Markov chains. We represent the conditional probability function as the sum of multi-linear memory function monomials of different orders (from zero up to the chain order). Read More

We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the Aubry-Andr\'{e} model by a sudden change of the strength of incommensurate potential $\Delta$ and unveil that the dynamical signature of localization-delocalization transition can be characterized by the occurrence of zero points in the Loschmit echo. For the quench process with quenching taking place between two limits of $\Delta=0$ and $\Delta=\infty$, we give analytical expressions of the Loschmidt echo, which indicate the existence of a series of zero points in the Loschmidt echo. For a general quench process, we calculate the Loschmidt echo numerically and analyze its statistical behavior. Read More

We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. Read More

We generalize the method of computing functional determinants with excluded zero mode developed by McKane and Tarlie to the differential operators with degenerate zero modes. We consider a $2\times 2$ matrix differential operator with two independent zero modes and show that its functional determinant can be expressed only in terms of these modes in the spirit of Gel'fand-Yaglom approach. Our result can be easily extended to the case of $N\times N$ matrix differential operators with $N$ zero modes. Read More

We introduce a wavefront shaping protocol for focusing inside disordered media based on a generalization of the established Wigner-Smith time-delay operator. The key ingredient for our approach is the scattering (or transmission) matrix of the medium and its derivative with respect to the position of the target one aims to focus on. A specifc experimental realization in the microwave regime is presented showing that the eigenstates of a corresponding operator are sorted by their focusing strength - ranging from strongly focusing on the designated target to completely bypassing it. Read More

Our everyday experience teaches us that the structure of a medium strongly influences how light propagates through it. A disordered medium, e.g. Read More

We study the coupling between conventional (Maxwell) and emergent electrodynamics in quantum spin ice, a 3+1-dimensional $U(1)$ quantum spin liquid. We find that a uniform electric field can be used to tune the properties of both the ground state and excitations of the spin liquid. In particular, it induces emergent birefringence, rendering the speed of the emergent light anisotropic and polarization-dependent. Read More

The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. Read More

We enquire into the quasi-many-body localization in topologically ordered states of matter, revolving around the case of Kitaev toric code on ladder geometry, where different types of anyonic defects carry different masses induced by environmental errors. Our study verifies that random arrangement of anyons generates a complex energy landscape solely through braiding statistics, which suffices to suppress the diffusion of defects in such multi-component anyonic liquid. This non-ergodic dynamic suggests a promising scenario for investigation of quasi-many-body localization. Read More

We present a non-perturbative analysis of the power-spectrum of energy level fluctuations in fully chaotic quantum structures. Focussing on systems with broken time-reversal symmetry, we employ a finite-$N$ random matrix theory to derive an exact multidimensional integral representation of the power-spectrum. The $N\rightarrow \infty$ limit of the exact solution furnishes the main result of this study -- a universal, parameter-free prediction for the power-spectrum expressed in terms of a fifth Painlev\'e transcendent. Read More

We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular we focus on the Aubry-Andr\'e-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a transparent and experimentally viable technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. Read More

The four-wave interaction in quantum nonlinear Schr\"odinger lattices with disorder is shown to destroy the Anderson localization of waves, giving rise to unlimited spreading of the nonlinear field to large distances. Moreover, the process is not thresholded in the quantum domain, contrary to its "classical" counterpart, and leads to an accelerated spreading of the subdiffusive type, with the dispersion $\langle(\Delta n)^2\rangle \sim t^{1/2}$ for $t\rightarrow+\infty$. The results, presented here, shed new light on the origin of subdiffusion in systems with a broad distribution of relaxation times. Read More

We reveal the role of fluctuations in percolation of sparse complex networks. To this end we consider two random realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in the giant component of the network in both cases or just in one case. Our framework includes a message-passing algorithm able to predict the fluctuations in a single network, and an analytic prediction of the expected fluctuations in ensembles of sparse networks. Read More

The Gr\"uneisen relation is shown to be important for the thermodynamics of dense liquids. Read More

We study the many-body localization of spin chain systems with quasiperiodic fields. We identify the lower bound for the critical disorder necessary to drive the transition between the thermal and many-body localized phase to be $W_{cl}\sim 1.85$, based on finite-size scaling of entanglement entropy and fluctuations of the bipartite magnetization. Read More

The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing the full quantum state from simple measurements, and therefore provides a key tool to obtain reliable analytics. Brute-force approaches to QST, however, demand resources growing exponentially with the number of constituents, making it unfeasible except for small systems. Read More

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for associative memory. In this equivalence, weights in the former play as patterns in the latter. Read More

The evident robustness of neural computation is hypothesized to arise from some degree of local stability around dynamically-generated sequences of local-circuit activity states involving many neurons. Recently, it was discovered that even randomly-connected cortical circuit models exhibit dynamics in which their phase-space partitions into a multitude of attractor basins enclosing complex network state trajectories. We provide the first theory of the random geometry of this disordered phase space. Read More

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether such scaling laws stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as systems poised at criticality have been argued to exhibit a number of important functional advantages. Here we employ a well-known model for neural dynamics with synaptic plasticity, to elucidate an alternative scenario in which neuronal avalanches can coexist, overlapping in time, but still remaining scale-free. Read More

Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission eigenchannels, producing dramatically different spatial intensity profiles. In contrast to the density of transmission eigenvalues that is dictated by the universal bimodal distribution, the spatial structures of the eigenchannels are not universal and depend on the confinement geometry of the system. Read More

We have created and studied artificial magnetic quasicrystals based on Penrose tiling patterns of interacting nanomagnets that lack the translational symmetry of spatially periodic artificial spin ices. Vertex-level degeneracy and frustration induced by the network topology of the Penrose pattern leads to a low energy configuration that we propose as a ground state. It has two parts, a quasi-one-dimensional rigid "skeleton" that spans the entire pattern and is capable of long-range order, and clusters of macrospins within it that are degenerate in a nearest neighbour model, and so are "flippable". Read More

We consider the spreading of the wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of non-ergodic extended states $1<\gamma<2$. We show that despite non-trivial fractal dimensions $0 < D_{q}=2-\gamma<1$ characterize wave function statistics in this region, the wave packet spreading $\langle r^{2} \rangle \propto t^{\beta}$ is governed by the "diffusion" exponent $\beta=1$ outside the ballistic regime $t>\tau\sim 1$ and $\langle r^{2}\rangle \propto t^{2}$ in the ballistic regime for $t<\tau\sim 1$. This demonstrates that the multifractality exhibits itself only in {\it local} quantities like the wave packet survival probability but not in the large-distance spreading of the wave packet. Read More

In the presence of strong homogeneous disorder, the superconducting state of an s-wave superconductor becomes fragmented, forming superconducting islands that are weakly coupled through insulating regions. Here, using a combination of electrical transport and low temperature scanning tunneling spectroscopy, we show that the application of magnetic field, has an effect similar to increasing the disorder strength. Starting with a weakly disordered NbN thin film ( Tc ~ 9K ), we show that under the application of magnetic field the superconducting state becomes increasingly granular, where lines of vortices separate the superconducting islands. Read More

We analyze quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. Read More

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Read More

Thermal conductivity of a model glass-forming system in the liquid and glass states is studied using extensive numerical simulations. We show that near the glass transition temperture, where the structural relaxation time becomes very long, the measured thermal conductivity decreases with increasing age. Secondly the thermal conductivity of the disordered solid obtained at low temperatures depends on the cooling rate with which it was prepared, with lower cooling rates leading to lower thermal conductivity. Read More

The emergent integrability of the many-body localized phase is naturally understood in terms of localized quasiparticles. As a result, the occupations of the one-particle density matrix in eigenstates show a Fermi-liquid like discontinuity. Here we show that in the steady state reached at long times after a global quench from a perfect density-wave state, this occupation discontinuity is absent, which is reminiscent of a Fermi liquid at a finite temperature, while the full occupation function remains strongly nonthermal. Read More

This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for different types of the free energy probability distribution functions. In the second part of the review we discuss the problems which are still waiting for their solutions. Read More

We present detailed characterization of a novel rare-earth selenide spinel, MgEr$_2$Se$_4$, which is shown to be one of the only spin ice materials outside the well-studied 227 pyrochlore oxide family. X-ray and neutron diffraction confirm a pyrochlore sublattice of Er$^{3+}$, and inelastic neutron scattering data reveal that the Er$^{3+}$ spins have a local Ising character. Spin ice signatures are observed in both heat capacity and magnetic diffuse scattering measurements. Read More

How atoms in covalent solids rearrange over a medium-range length-scale during amorphization is a long pursued question whose answer could profoundly shape our understanding on amorphous (a-) networks. Based on ab-intio calculations and reverse Monte Carlo simulations of experiments, we surprisingly find that even though the severe chemical disorder in a-GeTe undermined the prevailing medium range order (MRO) picture, it is responsible for the experimentally observed MRO. That this thing could happen depends on a novel atomic packing scheme. Read More

Why is it difficult to refold a previously folded sheet of paper? We show that even crease patterns with only one designed folding motion inevitably contain an exponential number of `distractor' folding branches accessible from a bifurcation at the flat state. Consequently, refolding a sheet requires finding the ground state in a glassy energy landscape with an exponential number of other attractors of higher energy, much like in models of protein folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems. As in these problems, we find that refolding a sheet requires actuation at multiple carefully chosen creases. Read More

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that persist at large large distances. Anti-phase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns, that invade the network as a whole. Read More

We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Read More

By considering the quantum dynamics of a transverse field Ising spin glass on the Bethe lattice at large and small transverse fields we observe the appearance of a many body localized region. The region is located within the region in which the system, when in equilibrium, is a spin glass. Accordingly, we conjecture that quantum dynamics inside the glassy region is split in an MBL and a delocalized (but not necessarily ergodic) region. Read More

Population annealing is a promising recent approach for Monte Carlo simulations in statistical physics, in particular for the simulation of systems with complex free-energy landscapes. It is a hybrid method, combining importance sampling through Markov chains with elements of sequential Monte Carlo in the form of population control. While it appears to provide algorithmic capabilities for the simulation of such systems that are roughly comparable to those of more established approaches such as parallel tempering, it is intrinsically much more suitable for massively parallel computing. Read More

We investigate the Anderson localization in non-Hermitian Aubry-Andr\'e-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. Read More

Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. Read More

Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. Chimeras - localized frequency synchrony patterns - are candidates for such states, but their spatial location has predominantly been considered fixed. We show that dynamical transitions of the location of frequency synchrony arise in paradigmatic phase oscillator networks through metastable chimeras joined by heteroclinic connections. Read More

In the present paper, using a replica analysis, we examine the portfolio optimization problem handled in previous work and discuss the minimization of investment risk under constraints of budget and expected return for the case that the distribution of the hyperparameters of the mean and variance of the return rate of each asset are not limited to a specific probability family. Findings derived using our proposed method are compared with those in previous work to verify the effectiveness of our proposed method. Further, we derive a Pythagorean theorem of the Sharpe ratio and macroscopic relations of opportunity loss. Read More

We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors, including periodic and irregular global spiking signals, as well as coherent oscillations, an unexpected form of synchronization. Our numerical results also show that the properties of the population firing rate depend on the size of the system, particularly its structure and average value over time. Read More

Effective gauge fields have allowed the emulation of matter under strong magnetic fields leading to the realization of Harper-Hofstadter, Haldane models, and led to demonstrations of one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by time-symmetry breaking. Due to the discovery of quantum search algorithms based on walks on graphs, recent work has discovered new implications the effect of time-reversal symmetry breaking has on the transport of quantum states and has brought with it a host of new experimental implementations. Read More

We consider a one-dimensional quantum system of an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential. Our choice of interaction is motivated by the spectral analysis of the XXZ quantum spin chain. The main result concerns a version of high-disorder Fock-space localization expressed here in the configuration space of hard-core particles. Read More

We demonstrate the existence of large phononic band gaps in designed hyperuniform (isotropic) disordered two-dimensional (2D) phononic structures of Pb cylinders in epoxy matrix. The phononic band gaps in hyperuniform disordered phononic structures are comparable to band gaps of similar periodic structures, for both out-of-plane and in-plane polarizations. A large number of localized modes is identified near the band edges, as well as, diffusive transmission throughout the rest of the frequency spectrum. Read More

The specific heat of toluene in glass and crystal states, has been measured both at low temperatures down to 1.8 K (using the thermal relaxation method) and in a wide temperature range up to the liquid state (using a quasiadiabatic continuous method). Our measurements therefore extend earlier published data to much lower temperatures, thereby allowing to explore the low temperature glassy anomalies in the case of toluene. Read More

We study the finite temperature (FT) phase transitions of two-dimensional (2D) $q$-states Potts models on the square lattice, using the first principles Monte Carlo (MC) simulations as well as the techniques of neural networks (NN). We demonstrate that the ideas from NN can be adopted to study these considered FT phase transitions efficiently. In particular, even with a simple NN constructed in this investigation, we are able to obtain the relevant information of the nature of these FT phase transitions, namely whether they are first order or second order. Read More

Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network, namely, the hierarchical lattice. Each oscillator has a natural frequency, drawn independently from a common probability distribution. Read More

The consequences of nonmagnetic-ion dilution for the pyrochlore family Y$_{2}$($M_{1-x}N_{x}$)$_{2}$O$_{7}$ ($M$ = magnetic ion, $N$ = nonmagnetic ion) have been investigated. As a first step, we experimentally examine the magnetic properties of Y$_{2}$CrSbO$_{7}$ ($x$ = 0.5), in which the magnetic sites (Cr$^{3+}$) are percolative. Read More

Many aspects of many-body localization (MBL) transitions remain elusive so far. Here, we propose a higher-dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model and show that it exhibits an MBL transition. The model on a bipartite lattice has $N$ Majorana fermions with SYK interactions on each site of $A$-sublattice and $M$ free Majorana fermions on each site of $B$-sublattice. Read More