无序系统与神经网络

We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and…

We investigate the parameter space of transformer models trained on protein sequence data using a statistical mechanics framework, sampling the loss landscape at varying temperatures by Langevin dynamics to characterize the low-loss…

Although the two-dimensional model of random networks of metallic nanowires or carbon nanotubes is widely used, it significantly overestimates the number of contacts between elements compared to quasi-three-dimensional models. This, within…

The unidirectional Hatano-Nelson chain serves as the fundamental non-Hermitian building block of the Su-Schrieffer-Heeger (SSH) model. We investigate its Anderson localization properties under diagonal binary disorder. For weak disorder,…

We propose a disorder-free one-dimensional single-particle Hamiltonian hosting an exact mobility edge (ME), placing the system outside the assumptions of no-go theorems regarding unbounded potentials. By applying a linear Stark potential…

Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…

The generation of complex states like multifractal critical states has been an outstanding challenge in both classical and quantum physics. Here we propose a general framework, termed the imaginary gauge phase imprint, allowing to engineer…

The bulk-edge correspondence principle, a cornerstone of topological physics, ensures that first-order topological systems host robust chiral edge states in two dimension. This was later extended to higher-order phases, where second-order…

Anderson (localization) transition is a universal wave phenomenon characterized by a disorder-induced quantum phase transition from extended to localized states, whereas the non-Hermitian skin effect is a generic feature of non-Hermitian…

We generalize the theory of supervised contrastive learning, previously applied to physical systems at equilibrium or steady state, to systems following any dynamics described by coupled ordinary differential equations. We show that if…

Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…

The non-Hermitian skin effect is an anomalous localization phenomenon induced by nonreciprocal dissipation and has attracted considerable attention in recent years both theoretically and experimentally. In this article, we review the…

Motivated by frustrated magnets and spin-liquid-candidate materials, we study the thermodynamics of a 2D geometrically frustrated magnet with vacancy defects. The presence of vacancies imposes significant constraints on the bulk spins,…

We investigate the anatomy and complexity of quantum states in Krylov space, in the ergodic and many-body localised (MBL) phases of a disordered, interacting spin chain. The Krylov basis generated by the Hamiltonian from an initial state…

We introduce and solve a teacher-student formulation of the symmetric binary Perceptron, turning a traditionally storage-oriented model into a planted inference problem with a guaranteed solution at any sample density. We adapt the…

We introduce the non-Hermitian mosaic Maryland model, where a discrete modulation period and a non-Hermitian phase are incorporated into the potential, rendering the originally exactly solvable system generally non-integrable. This model…

Recently proposed analog solvers based on dynamical systems, such as Ising machines, are promising platforms for large-scale combinatorial optimization. Yet, given the heuristic nature of the field, there is very limited insight on…

An atomistic structural model for melt-quenched B$_2$O$_3$ glass has eluded the simulation community so far. The difficulty lies in the abundance of the six-membered boroxol rings - an intermediate-range order motif suggested through Raman…

We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient…

Building on recent progress in the study of Anderson and many-body localization via the renormalization group (RG), we examine the scaling theory of localization in the quantum Random Energy Model (QREM). The QREM is known to undergo a…