相关论文: Summing graphs for random band matrices

Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…

The statistics of random band--matrices with width and strength of the band slowly varying along the diagonal is considered. The Dyson equation for the averaged Green function close to the edge of spectrum is reduced to the Painlev\'{e} I…

We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in…

We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…

We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…

Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…

The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…

The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…

A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation…

We study a new class of matrix models, formulated on a lattice. On each site are $N$ states with random energies governed by a Gaussian random matrix Hamiltonian. The states on different sites are coupled randomly. We calculate the density…

The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…

Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary…

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…

The bulk boundary correspondence, one of the most significant features of topological matter, theoretically connects the existence of edge modes at the boundary with topological invariants of the bulk spectral bands. However, it remains…

This paper adapts the recently developed rigorous application of the supersymmetric transfer matrix approach for the 1d band matrices to the case of the orthogonal symmetry. We consider $N\times N$ block band matrices consisting of $W\times…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…