无序系统与神经网络

We investigate the phase diagram and memory retrieval capabilities of bipartite energy-based neural networks, namely Restricted Boltzmann Machines (RBMs), as a function of the prior distribution imposed on their hidden units - including…

Square Wave Perceptrons (SWPs) form a class of neural network models with oscillating activation function that exhibit intriguing ``hardness'' properties in the high-dimensional limit at a fixed constraint density $\alpha = O(1)$. In this…

We investigate the shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble,…

The spectra of particles in disordered lattices can either be completely extended or localized or can be intermediate which hosts both the localized and extended states separated from each other. In this work, however, we show that in the…

Deep neural networks (DNNs) exhibit crackling-like avalanches whose origin lacks a mechanistic explanation. Here, I derive a stochastic theory of deep information propagation (DIP) by incorporating Central Limit Theorem (CLT)-level…

Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…

Rydberg atom arrays promise high-fidelity quantum simulations of critical phenomena with flexible geometries. Yet experimental realizations inevitably suffer from disorder due to random displacements of atoms, leading to departures from the…

We investigate the Holstein mechanism in a single-electron (one-site) system, where unitary evolution intrinsically involves both fermion and boson operators under nonadiabatic conditions. The resulting unitary dynamics and boson-frequency…

We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat 2D space. We first prove that any rotationally symmetric 2D membrane…

The impact of disorder on wave transport has been extensively studied in Hermitian systems, where static randomness gives rise to Anderson localization. In non-Hermitian lattices, static disorder can lead to peculiar transport features,…

One among the most intriguing results coming from the application of statistical mechanics to the study of brain is the understanding that it, as a dynamical system, is inherently out of equilibrium. In the realm of non-equilibrium…

We study the critical behavior of the Ising spin glass in five spatial dimensions through large-scale Monte Carlo simulations and finite-size scaling analysis. Numerical evidence for a phase transition is found both with and without an…

Non-Hermitian systems with non-reciprocal hopping may display the non-Hermitian skin effect, where states under open boundary conditions localize exponentially at one edge of the system. This localization has been linked to spectral winding…

A novel localization phenomenon, termed erratic non-Hermitian skin localization, has been identified in disordered globally-reciprocal non-Hermitian lattices. Unlike conventional non-Hermitian skin effect and Anderson localization, it…

Phenomena including friction and earthquakes are complicated by the joint presence of disorder and non-linear instabilites, such as those triggered by the presence of velocity weakening. In [de Geus and Wyart, Phys. Rev. E 106, 065001…

We introduce a class of models containing robust and analytically demonstrable multifractality induced by disorder correlations. Specifically, we investigate the statistics of eigenstates of disordered tight-binding models on two classes of…

The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…

Accurate grain orientation mapping is essential for understanding and optimizing the performance of polycrystalline materials, particularly in energy-related applications. Lithium nickel oxide (LiNiO$_{2}$) is a promising cathode material…

Recently, thanks to the development of artificial intelligence (AI) there is increasing scientific attention in establishing the connections between theoretical physics and AI. Traditionally, these connections have been focusing mostly on…

Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals.…