无序系统与神经网络

By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium…

We establish a phase diagram of a model in which scalar waves are scattered by resonant point scatterers pinned at random positions in the free three-dimensional (3D) space. A transition to Anderson localization takes place in a narrow…

We use two different fully vectorial microscopic models featuring nonresonant and resonant scattering, respectively, to demonstrate the Anderson localization transition for elastic waves in three-dimensional (3D) disordered solids. Critical…

The microscopic dependence of glassy equilibration on sample history, both the initial configuration and the specific sequence of random noise, is examined. The temporal evolution of spin configurations in a two-dimensional Ising spin glass…

Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…

We demonstrate that an aperiodic array of certain quantum networks comprising magnetic and non-magnetic atoms can act as perfect spin filters for particles with arbitrary spin state. This can be achieved by introducing minimal quasi-one…

We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…

In two dimensional disordered lattices, presence of interaction makes particles less localized than the non-interacting ones within the range of disorder strength $W \le 4$ and interaction strength $V \le 4$. If the interaction strength is…

We relate the structure factor $S(\mathbf{k} \to \mathbf{0})$ in a system of jammed hard spheres of number density $\rho$ to its complexity per particle $\Sigma(\rho)$ by the formula $S(\mathbf{k} \to \mathbf{0})=-1/…

We investigate the thermodynamic properties of a Restricted Boltzmann Machine (RBM), a simple energy-based generative model used in the context of unsupervised learning. Assuming the information content of this model to be mainly reflected…

Dynamical structure factor (S(k,$\omega$)) is calculated for the one-dimensional (1D) transverse field Ising model, and its recent extension to include a three spin term, with quenched binary disorder. We study the low energy modes for…

Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…

A recent description of the highly viscous flow ascribes it to irreversible thermally activated Eshelby transitions, which transform a region of the undercooled liquid to a different structure with a different elastic misfit to the…

For planar and cubic Ising models, we examined two ways of approximation of a spectral density that describes a degeneracy of energy levels. We approximated the exponent of the spectral density by polynomials of even degrees and using our…

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…

Local observables in generic periodically driven closed quantum systems are known to relax to values described by periodic infinite temperature ensembles. At the same time, ergodic static systems exhibit anomalous thermalization of local…

We have performed studies of the 3D random field $XY$ model on $L \times L \times L$ simple cubic lattices with periodic boundary conditions, with a random field strength of $h_r$ = 1.875, for $L = 64$ and $L = 96$, using a parallelized…

The function space of deep-learning machines is investigated by studying growth in the entropy of functions of a given error with respect to a reference function, realized by a deep-learning machine. Using physics-inspired methods we study…

We study the influence of spinless impurities on a frustrated magnet featuring a spin-density wave (stripe) phase by means of Monte Carlo simulations. We demonstrate that the interplay between the impurities and an order parameter that…

We discuss the effects of the localized modes on the density of state $D(\omega)$ by introducing the probability distribution function of the proximity to the marginal stability. Our theoretical treatment reproduces the numerical results in…