无序系统与神经网络

The brain criticality hypothesis has largely only characterized brain dynamics in terms of their self-similarity, although experimental evidence suggests that the brain exhibits significant multifractality. To understand how multifractality…

We study the connected ensemble, a statistical-mechanics framework that characterizes the formation of low-loss paths in rugged landscapes. First introduced in a previous paper, this ensemble allows one to identify when a network can be…

Machine Learning (ML) has deeply changed some fields recently, like Language and Vision and we may expect it to be relevant also to the analysis of of complex systems. Here we want to tackle the question of how and to which extent can one…

Restricted Boltzmann Machines (RBMs) are generative models designed to learn from data with a rich underlying structure. In this work, we explore a teacher-student setting where a student RBM learns from examples generated by a teacher RBM,…

The ultraslow dynamics of glass-formers has been explained by two views considered as mutually exclusive: one invokes locally hindered mobility, the other rests on the complexity of the configuration space. Here we demonstrate that the…

Anderson localization is a phase transition between a metallic phase, where wavefunctions are extended and delocalized in space, and an insulating phase, where wavefunctions are completely localized. These transitions are driven by…

Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…

Solving the quantum many-body ground state problem remains a central challenge in computational physics. In this context, the Variational Monte Carlo (VMC) framework based on Projected Entangled Pair States (PEPS) has witnessed rapid…

Anderson localization admits a complete symmetry classification given by the Altland-Zirnbauer (AZ) tenfold scheme, whereas an analogous framework for interacting many-body localization (MBL) has remained elusive. Here we develop a…

Localization is a pervasive phenomenon across physics, shaping transport from electrons in solids to light and sound in engineered media. In traditional settings, disorder strongly impedes transport, resulting in dynamical localization or,…

Exceptional points (EPs) are spectral degeneracies unique to non-Hermitian systems which underpin phenomena from enhanced sensing to unconventional topology. While disorder is usually viewed as detrimental, it can also drive topological…

We use the Binary Intrinsic Dimension (BID), a geometrical measure designed for binary data, to analyze the Hopfield model, a paradigmatic spin system from statistical mechanics, machine learning and neuroscience. The BID allows us to…

The process of dephasing during wave evolution has traditionally been viewed as an obstacle to localization, leading to diffusion even in strongly disordered Hermitian lattices. In contrast, here we demonstrate how the interplay of…

We study a one-dimensional quasiperiodic tight-binding model with simultaneous off-diagonal (hopping) and diagonal (onsite) modulations. Using the inverse participation ratio and the wave-packet centroid, we construct…

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we…

Localization of coherent propagating waves has been extensively studied over the years, primarily in homogeneous random media. However, significantly less attention has been given to wave localization in inhomogeneous systems, where the…

We study a stroboscopic quantum Ising model with Fibonacci dynamics. Focusing on boundary spin correlation functions in long but finite chains, our simulations as well as analytical arguments reveal a self-similar phase diagram exhibiting…

We address the fate of many-body localization (MBL) of mid-spectrum eigenstates of a matter-free $U(1)$ quantum-link gauge theory Hamiltonian with random couplings on ladder geometries. Apart from level spacing distribution indicators like…

Motivated by an experiment on a superconducting quantum processor [Mi et al., Science 378, 785 (2022)], we study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The pairings derive from Majorana…

Complex systems of many interacting components exhibit patterns of recurrence and emergent behaviors in their time evolution that can be understood from a new perspective of physics of information dynamics, modeled after one such system,…