Eigenvalue Correlations For Banded Matrices

Details Eigenvalue Correlations For Banded Matrices Eigenvalue Correlations For Banded Matrices

1998-12-15

arxiv.org/abs/cond-mat/9812239v1

Physics

Condensed Matter

Statistical Mechanics

Latex file, 5 pages, No figures

Scientific paper

We study the evolution of the distribution of eigenvalues of $N\times N$ 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 $N\times N$ 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.

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