无序系统与神经网络

Complexity is a measure of information content. Crystalline materials are not complex systems because their structures can be represented tersely using the language of crystallography. Disordered materials are also structurally simple if…

We study infinite resistor networks perturbed by line defects, in which the resistances are periodically modified along a single line. Using the Sherman-Morrison identity applied to the reciprocal-space representation of the lattice Green's…

The mobility edge (ME) is a fundamental concept in the Anderson localized systems, which marks the energy separating extended and localized states. Although the ME and localization phenomena have been extensively studied in non-Hermitian…

We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined…

Recently, the driven dynamics of localization phase transitions have garnered growing interest. However, studies so far have mainly considered initial localized states, whose driven dynamics follow the Kibble-Zurek mechanism (KZM). In this…

The physics of localized states in quasiperiodic lattices has been extensively studied for decades, but still lacks an comprehensive theoretical framework. Recently, we developed a incommensurate energy band (IEB) theory, which extends the…

The driven dynamics of localization transitions in a non-Hermitian Disordered Aubry-Andr\'{e} (DAA) model are examined under both open boundary conditions (OBC) and periodic boundary conditions (PBC). Through an analysis of the static…

We apply a recently developed theory of the nonphononic vibrational density of states (DOS) in glasses to investigate the impact of local frozen-in stresses on the low-temperature specific heat. Using a completely harmonic description we…

In this study, we demonstrate that the vacuum itself suffices to delocalize an Anderson insulator inside a cavity. By studying a disordered one-dimensional spinless fermion system coupled to a single photon mode describing the vacuum…

Quasiperiodic systems are known to exhibit localization transitions in low dimensions, wherein all electronic states become localized beyond a critical disorder strength. Interestingly, recent studies have uncovered a reentrant localization…

Deep artificial neural networks have surpassed human-level performance across a diverse array of complex learning tasks, establishing themselves as indispensable tools in both social applications and scientific research. Despite these…

Disorder and non-Hermitian effects together can upend how waves localize. In a 1D disordered chain, the non-Hermitian skin effect (NHSE) can induce Anderson delocalization, defying the usual rule that disorder in low dimensions always…

Eigenstate multifractality, a hallmark of non-interacting disordered metals, which may also be observed in many-body localized states, is characterized by anomalous slow dynamics and appears relevant for many areas of quantum physics, from…

Feature extraction - the ability to identify relevant properties of data - is a key factor underlying the success of deep learning. Yet, it has proved difficult to elucidate its nature within existing predictive theories, to the extent that…

The recent development of the calculation of specific heat ($C$) of liquids and glasses by first-principles molecular dynamics (MD) simulations is reviewed. Liquid and glass states have common properties in that there is no periodicity and…

The boson peak (BP) stands as a key feature in understanding glasses and amorphous materials. It directly underlies their anomalous material properties, including thermal behaviors such as excess specific heat and low thermal conductivity,…

The remarkable universality of the eigenvalue correlation functions is perhaps one of the most salient findings in random matrix theory. Particularly for short-range separations of the eigenvalues, the correlation functions have been shown…

We study nonequilibrium quantum dynamics of spin chains by employing principal component analysis (PCA) on data sets of wave function snapshots and examine how information propagates within these data sets. The quantities we employ are…

We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the…

We use heuristic optimization methods in extensive computations to determine with low systematic error ground state configurations of the mean-field $p$-spin glass model with $p=3$. Here, all possible triplets in a system of $N$ Ising spins…