Eigenvalue Correlations For Banded Matrices

Дата и время публикации : 1998-12-15T04:10:57Z

Авторы публикации и институты :
Pragya Shukla

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: Latex file, 5 pages, No figures
Первичная категория: cond-mat.stat-mech

Все категории : cond-mat.stat-mech

Краткий обзор статьи: We study the evolution of the distribution of eigenvalues of $Ntimes N$ 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 $Ntimes N$ 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.

Category: Physics