Non-Gaussian random-matrix ensembles with banded spectra

Abstract

Non-Gaussian random-matrix ensembles are important in many applications. We propose Monte Carlo and Langevin methods for generating non-Gaussian ensembles and their eigenvalue spectra. We also provide a general framework for analytic studies of the level density in these ensembles. We show that, in general, the level densities exhibit banded spectra, with important implications for mesoscopic systems and complex nuclei. The universality of energy-level fluctuations is confirmed.

Universal spectral correlations in ensembles of random normal matrices

“…We study the two-eigenvalue and higher order correlations as well as spacing distribution to show that unfolded spectra are stationary and universal. We confirm our results by Monte Carlo (MC) simulation [25] of several non-gaussian ensembles. As an application, we also study effect of dissipation on the quantum kicked rotor maps [26][27][28].…”

Long-range interactions in the quantum many-body problem in one dimension: Ground state

“…of eigenvalues of non-Gaussian ensembles of random matrices. Using the polynomial method developed by Ghosh and Pandey in the context of random matrix theory (RMT) [14,15], we observe band structure [16] in the particle density, which in turn corresponds to the density of zeros of the corresponding polynomials [7,14,15]. For a given value of the interaction strength, we study the PCF for different interparticle spacings.…”

“…For E 0 > E 0c , we observe the formation of two bands in particle density. Rescaling the result obtained by Pandey [16], we get…”

Random matrix ensembles: Wang-Landau algorithm for spectral densities

“…The solid lines represent the results from the Wang-Landau simulation. For comparison we also show the results of Monte Carlo simulation based on Boltzmann sampling [6]. Fig.…”

“…In addition, the numerical simulation of spectra facilitates the verification of known analytical results. The conventional numerical schemes for generating eignvalue densities rely on either the diagonalisation approach using the matrix model whenever available, or implementing the Boltzmann-sampling-based Monte Carlo simulation [6]. The latter uses Dyson's log-gas picture for the eigenvalues of RME [1,7].…”