1998/12/15 by Pragya Shukla, Shukla, Pragya
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Matrix Theory and Algorithms #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9812239
Latex file, 5 pages, No figures
arxiv created 1998/12/15 · openalex publication_date 1998/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the evolution of the distribution of eigenvalues of N× N matrix ensembles subject to a change of variances of its matrix elements. Our results indicate that the evolution of the probability density is governed by a Fokker- Planck equation similar to the one governing the time-evolution of the particle- distribution in Wigner-Dyson gas, with relative variances now playing the role of time. This is also similar to the Fokker-Planck equation for the distribution of eigenvalues of a N× N matrix subject to a random perturbation taken from the standard Gaussian ensembles with perturbation-strength as the "time" variable. This equivalence alonwith the already known correlations of standard Gaussian ensembles can therefore help us to obtain the same for various physically-significant cases modeled by random banded Gaussian ensembles.