Related papers: Interaction of Regular and Chaotic States
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although…
Random band matrices relevant for open chaotic systems are introduced and studied. The scattering model based on such matrices may serve for the description of preequilibrium chaotic scattering. In the limit of a large number of open…
We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
For $m$ number of bosons, carrying spin ($S$=1) degree of freedom, in $\Omega$ number of single particle orbitals, each triply degenerate, we introduce and analyze embedded Gaussian orthogonal ensemble of random matrices generated by random…
We identify the chaotic phase of the Bose-Hubbard Hamiltonian by the energy-resolved correlation between spectral features and structural changes of the associated eigenstates as exposed by their generalized fractal dimensions. The…
A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics whereas those of time-reversal symmetric,…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
A known result in random matrix theory states the following: Given a random Wigner matrix $X$ which belongs to the Gaussian Orthogonal Ensemble (GOE), then such matrix $X$ has an invariant distribution under orthogonal conjugations. The…
We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient…
A rotationally invariant random interaction ensemble was realized in a single-j fermion model. The dominance of ground states with zero and maximum spin was confirmed and explained with a statistical approach based on the random coupling of…
We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
The distortion of the regular motion in a quantum system by its coupling to the continuum of decay channels is investigated. The regular motion is described by means of a Poissonian ensemble. We focus on the case of only few channels K<10.…
We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the…
We study the RPA equations in their most general form by taking the matrix elements appearing in the RPA equations as random. This yields either a unitarily or an orthogonally invariant random-matrix model which is not of the Cartan type.…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
High resolution experiments have recently lead to a complete identification (energy, spin, and parity) of 151 nuclear levels up to an excitation Energy of Ex= 6.20 MeV in 208Pb. We present a thorough study of the fluctuation properties in…
As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are…