无序系统与神经网络

Motivated by many contemporary problems in condensed matter physics where matter particles experience random gauge fields, we investigate the physics of fermions on a square lattice with $\pi$-flux (that realizes Dirac fermions at low…

Self-similarity, where observables at different length scales exhibit similar behavior, is ubiquitous in natural systems. Such systems are typically characterized by power-law correlations and universality, and are studied using the…

The graphicality problem -- whether or not a sequence of integers can be used to create a simple graph -- is a key question in network theory and combinatorics, with many important practical applications. In this work, we study the…

In this study, novel exact solutions of the Duffing equation with their phase portraits have been proposed and reasoned. It is shown that phase trajectories are initially elliptical and become distorted in the unstable area within the…

Quantum topology categorizes physical systems in integer invariants, which are robust to some deformations and certain types of disorder. A prime example is the Su-Schrieffer-Heeger (SSH) model, which has two distinct topological phases,…

We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

Recent work that analyzed the effect of vacancy disorder on a short-range resonating valence bond spin liquid state of kagome-lattice antiferromagnets argued that such spin liquids are stable to vacancy disorder. The argument relied…

We introduce a conceptual reformulation of the Mott-Berezinski\u{i} (MB) theory of low-frequency AC conductivity in disordered systems based on localization landscape theory. Instead of assuming uniform localization and fixed hopping…

Classical approaches to ecological stability rely on fully connected interaction models, yet real ecosystems are sparse and structured--a feature that qualitatively reshapes their collective dynamics. Here, we establish a thermodynamically…

We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…

We study the learning dynamics of the soft committee machine (SCM) with Rectified Linear Unit (ReLU) activation using a statistical-mechanics approach within the annealed approximation. The SCM consists of a student network with $N$ input…

Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic…

Quasiperiodic models are important physical platforms to explore Anderson transitions in low dimensional systems, yet the exact mobility edges (MEs) are generally hard to be determined analytically. To date, the MEs in only a few models can…

In one-dimensional quasiperiodic systems, only a few models with exact mobility edges (MEs) have been constructed using generalized self-duality theory, Avila's global theory, or the renormalization group method. This raises an intriguing…

We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths,…

Organic mixed conductors (OMCs) represent a promising class of materials for applications in bioelectronics, physical computing, and thermoelectrics. Rather unparalleled, OMCs feature dynamics spanning multiple length and time scales,…

We introduce an analytical framework to calculate the values of key observables in a strongly disordered discrete time crystal (DTC) without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement…

Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…

We consider the problem of isotropic effective conductivity $\sigma_e(\sigma_1,\ldots,\sigma_n)$ in two-dimensional three- and four-phase symmetric composites with a partial isotropic conductivity $\sigma_j$ of the $j$-th phase. The upper…