无序系统与神经网络
Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive…
An important component of the success of large AI models is double descent, in which networks avoid overfitting as they grow relative to the amount of training data, instead improving their performance on unseen data. Here we demonstrate…
Phase transitions in one-dimensional lattice systems are well established and have been extensively studied within both Hermitian and non-Hermitian frameworks. In this work, we extend this understanding to a more general setting by…
Ergodic isolated quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH), i.e., the expectation values of local observables in the system's eigenstates approach the predictions of the microcanonical ensemble.…
We explore properties of a Gross-Pitaevskii chain subject to an incommensurate periodic potential, i.e., a nonlinear Aubry-Andre model. We show that the condensate crucially impacts the properties of the elementary excitations. In contrast…
This paper introduces a learning framework for Three-Directional Associative Memory (TAM) models, extending the classical Hebbian paradigm to both supervised and unsupervised protocols within an hetero-associative setting. These neural…
We investigate a phase transition from linear to nonlinear information processing in echo state networks, a widely used framework in reservoir computing. The network consists of randomly connected recurrent nodes perturbed by a noise and…
The problem of a single Hermitian impurity has long served as a cornerstone in condensed matter physics, offering fundamental insights into the mechanisms of Anderson localization. Yet, despite the increased interest in the spectral and…
Place-cell networks, typically forced to pairwise synaptic interactions, are widely studied as models of cognitive maps: such models, however, share a severely limited storage capacity, scaling linearly with network size and with a very…
Oxide glasses have proven to be useful across a wide range of technological applications. Nevertheless, their medium-range structure has remained elusive. Previous studies focused on the ring statistics as a metric for the medium-range…
A generalized version of the Wilson-Cowan (WC) model is proposed which accounts for the evolution of the synaptic resources. Adiabatic elimination of the fast variables is performed to yield a simplified framework for the coupled…
Localization transitions represent a fundamental class of continuous phase transitions, yet they occur without any accompanying symmetry breaking. We resolve this by introducing the concept of dynamical translational symmetry (DTS), which…
The experiments performed with neutral atoms trapped in optical tweezers and coherently coupled to the Rydberg state allow quantum simulations of paradigmatic Hamiltonians for quantum magnetism. Previous studies have focused mainly on…
We study the dynamics of the generalized Lotka-Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us…
The simulation of borosilicate glasses is challenging due to the composition and temperature dependent coordination state of boron atoms. Here, we present a newly developed machine learning optimized classical potential for molecular…
Charge transport in QD solids is typically understood as thermally activated tunneling or hopping between states that are localized on individual QDs. Here, we show that the slow relaxation that is associated with the disorder-broadened…
We study the equilibrium glassy behavior of a multimode random laser model with nonlinear four-body quenched disordered interactions and a global smoothed-cubic constraint on mode intensities. This constraint, which provides a more…
We investigate a generalized Aubry-Andr\'{e}-Harper (AAH) model with non-reciprocal hopping and power-law quasiperiodic potentials $V(i) = V\left[ \cos(2\pi \beta i) \right]^p$. Our study reveals that the interplay between nonreciprocity,…
Typically, scaling up the size of a system does not change the shape of its energy spectrum, other than making it denser. Exceptions, however, occur in the new phenomenon of non-Hermitian skin criticality, where closely competing…
The charge carrier localization length {\alpha} is a crucial, yet often ignored parameter of conjugated polymers that exponentially influences electronic conductivity. Here, we argue it is a unique proxy of the energy landscape as…