Universal singularity at the closure of a gap in a random matrix theory

Details Universal singularity at the closure of a gap in a random matrix theory Universal singularity at the closure of a gap in a random matrix theory

1998-04-03

arxiv.org/abs/cond-mat/9804023v1

Physics

Condensed Matter

Statistical Mechanics

20pages, Revtex, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.57.4140

We consider a Hamiltonian $ H = H_0+ V $, in which $ H_0$ is a given non-random Hermitian matrix,and $V$ is an $N \times N$ Hermitian random matrix with a Gaussian probability distribution.We had shown before that Dyson's universality of the short-range correlations between energy levels holds at generic points of the spectrum independently of $H_{0}$. We consider here the case in which the spectrum of $H_{0}$ is such that there is a gap in the average density of eigenvalues of $H$ which is thus split into two pieces. When the spectrum of $H_{0}$ is tuned so that the gap closes, a new class of universality appears for the energy correlations in the vicinity of this singular point.

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