无序系统与神经网络

The analysis of complex systems such as neural networks is made particularly difficult by the overwhelming number of their interacting components. In the absence of prior knowledge, identifying a small but informative subset of network…

The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks…

We investigate the influence of quasiperiodic modulations on one-dimensional non-Hermitian diamond lattices with an artificial magnetic flux $\theta$ that possess flat bands. Our study shows that the symmetry of these modulations and the…

In the presence of quenched disorder, the interplay between local magnetic-moment formation and Anderson localization for electrons at a zero-temperature, metal-insulator transition (MIT) remains a long unresolved problem. Here, we study…

It is generally believed (but not yet proved) that Ising spin glasses with nearest-neighbor interactions have a phase transition in three and higher dimensions to a low-temperature spin glass phase, but the nature of this phase remains…

Motivated by the wide presence of multilayer networks in both natural and human-made systems, within a random matrix theory (RMT) approach, in this study we compute eigenfunction and spectral properties of multilayer directed random…

Hebbian learning theory is rooted in Pavlov's Classical Conditioning. While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently it has been numerically shown…

We investigate the critical behavior and the dynamics of the amplitude (Higgs) mode close to the superfluid-insulator quantum phase transition in an amorphous system (i.e., a system subject to topological randomness). In particular, we map…

The classic paradigms for learning and memory recall focus on strengths of synaptic couplings and how these can be modulated to encode memories. In a previous paper [A. K. Behera, M. Rao, S. Sastry, and S. Vaikuntanathan, Physical Review X…

The human brain is a complex system that is fascinating scientists since a long time. Its remarkable capabilities include categorization of concepts, retrieval of memories and creative generation of new examples. At the same time, modern…

Fine resolution of the discrete eigenvalues at the spectral edge of an $N\times N$ random matrix is required in many applications. Starting from a finite-size scaling ansatz for the Stieltjes transform of the maximum likelihood spectrum, we…

We present a solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. It is achieved using a cavity or message passing approach, which allows one to…

The multifractal critical phase (MCP) fundamentally differs from extended and localized phases, exhibiting delocalized distributions in both position and momentum spaces. The investigation on the MCP has largely focused on one-dimensional…

Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil new fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are…

Quantum non-locality is an important concept in quantum physics. In this work, we study the quantum non-locality in a fermion many-body system under quasi-periodic disorders. The Clauser-Horne-Shimony-Holt (CHSH) inequality is…

We make lattice generalization of two well-known zero-dimensional models of quantum spin glass, Sachdev-Ye (SY) and spherical quantum $p$-spin glass model, to one dimension for studying crossovers in non-local scrambling dynamics due to…

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction…

Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e. bipartite networks between nodes and factor nodes (representing groups of nodes).…

We explore the structural signatures of excitations in amorphous materials with the atomic cluster expansion (ACE), a universal and complete linear basis of descriptors of the atomic environment. Body-orderd linear classifiers are…

Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for…