无序系统与神经网络

Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, R\'enyi entropy, a one-parameter…

We investigate two one-dimensional tight-binding models with disorder that have extended states at zero energy. We use exact and partial diagonalisation of the Hamiltonian to obtain the eigenmodes and the associated participation ratios,…

The rapid advancement of environmental sequencing technologies, such as metagenomics, has significantly enhanced our ability to study microbial communities. The eubiotic composition of these communities is crucial for maintaining ecological…

We discuss the dependence of the critical properties of the Anderson model on the dimension $d$ in the language of $\beta$-function and renormalization group recently introduced in Ref.[arXiv:2306.14965] in the context of Anderson…

Using computer simulation, we investigated the dependence of the electrical conductivity of random two-dimensional systems of straight nanowires on the main parameters. Both the resistance of the conductors and the resistance of the…

In the last few years, several works have identified the concurrence of the spectral, delocalization-localization and topological phase transitions in non-Hermitian quasiperiodic systems in the presence of time-reversal symmetry (TRS), with…

We show that Oscillator Ising Machines (OIMs) are prime candidates for use as neuromorphic machine learning processors with Equilibrium Propagation (EP) based on-chip learning. The inherent energy gradient descent dynamics of OIMs, combined…

Many-body-localization (MBL) transitions are studied in a family of single-spin-flip spin-$\frac12$ models, including the one-dimensional (1D) chain with nearest-neighbor interactions, the quantum dot (QD) model with all-to-all pair…

Topological Anderson insulators (TAIs) provide a mechanism for topological phase transitions in disordered systems and have implications for quantum material design. In this work, we investigate the emergence of multiple TAIs in a…

In the context of the Many-Body-Localization phenomenology we consider arbitrarily large one-dimensional local spin systems, the XXZ model with random magnetic field is a prototypical example. Without assuming the existence of exponentially…

Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a family of 2D models generalizing recent experiments on photonic…

We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-$\frac{1}{2}$ systems. Our formalism is suitable for systems with $\textrm{U}(1)$…

Comprehending sound damping is integral to understanding the anomalous low temperature properties of glasses. Despite decades of studies, the underlying mechanism of sound damping in glasses is still debated. In this perspective we review…

We study sign structures of the ground states of spin-$1/2$ magnetic systems using the methods of Boolean Fourier analysis. Previously it was shown that the sign structures of frustrated systems are of complex nature: specifically, neural…

We investigate the role of relaxation mechanisms in the driven response of elastic disordered interfaces in finite dimensions, focusing on the interplay between dimensionality and interaction range. Through extensive numerical simulations,…

This work presents a statistical mechanics characterization of neural networks, motivated by the replica symmetry breaking (RSB) phenomenon in spin glasses. A Hopfield-type spin glass model is constructed from a given feedforward neural…

Auxetic metamaterials are commonly thought to exhibit favorable mechanical properties, notably high energy absorption. Here we investigate disordered metamaterials obtained from random beam networks by optimizing simultaneously auxeticity…

We investigate generalized Aubry-Andr\'{e} models featuring tunable quasidisordered potentials and a mobility edge that separates extended and localized states, with critical states for the mobility edge confirmed through finite-size…

In these notes we discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms:…

Computing gradients of a cost function is central to design-based optimization and machine learning algorithms. Equilibrium propagation provides an exact method to compute gradients in hardware by exploiting the inherent physical laws. The…