无序系统与神经网络

We introduce DOMINO, a light-matter computing platform that exploits the full complex amplitude of coupled condensate networks to solve maximum-weight clique problems and reveal hidden indirect correlations in large graphs. By embedding…

We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…

Expressions for the density of states $D(E)$, where $D(E)$ is the number of states of energy $E$, are well known. The present paper offers the expressions for generalized density of states $D_N(E,m)$, where $D_N(E,m)$ is the number of…

Despite decades of research, the universal nature of fluctuations in disordered quantum systems remains poorly understood. Here, we present extensive numerical evidence that fluctuations in two-dimensional (2D) Anderson localization belongs…

This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…

We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…

Non-deterministic polynomial-time (NP) problems are ubiquitous in almost every field of study. Recently, all-optical approaches have been explored for solving classic NP problems based on the spin-glass Ising Hamiltonian. However, obtaining…

We revisit the U(1) quantum link model in a ladder geometry, finding, by finite-size scaling, that the critical exponent $\nu=1$ and the central charge $c=1/2$ are consistent with the Ising universality class for all phase transitions…

Granular gases are commonly characterized through their velocity distribution, which provides access to the granular temperature. In experiments, velocity distributions are typically obtained by particle tracking, which however becomes…

Standard scaling theory dictates that disorder leads to immediate localization in one-dimensional Hermitian systems. We demonstrate that non-Hermitian topology fundamentally alters this paradigm, protecting transport up to a substantial…

Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a…

The quench dynamics of glassy systems are challenging. Due to aging, the system never reaches a stationary state but instead evolves on emergent scales that grow with its age. This slow evolution complicates field-theoretic descriptions, as…

We introduce and implement a reformulation of the strong disorder renormalization group method in real space, well suited to study bond disordered antiferromagnetic power law coupled quantum spin chains. We derive the Master equations for…

In this work, we investigate the combined effects of Rashba spin-orbit coupling (RSOC) and non-Hermiticity on topological phase transitions in spinful p-wave Kitaev chains. While previous studies have separately examined non-Hermitian (NH)…

Many-body localization (MBL) is understood theoretically through the existence of an extensive number of local integrals of motion (LIOMs). These conserved quantities are related to the microscopic quantum degrees of freedom that are…

Two-dimensional (2D) Dirac fermions occur ubiquitously in condensed matter systems from topological phases to quantum critical points. Since the advent of topological semimetals, where the dispersion is often tilted around the band crossing…

Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body…

The analytical solution to the out-of-equilibrium dynamics of mean-field spin glasses has profoundly shaped our understanding of glassy dynamics, which take place in many diverse physical systems. In particular, the idea that during the…

We propose a novel renormalization group (RG) method for non mean-field models of spin glasses, which leads to the emergence of a novel order parameter. Unlike previous approaches where the RG procedure is based on a priori notions on the…

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising tool for fluid dynamics, particularly for flow reconstruction and parameter identification. In the context of granular media, accurately estimating rheological…