Abstract
We consider a Hamiltonian , in which is a given nonrandom Hermitian matrix, and is an 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 . We consider here the case in which the spectrum of is such that there is a gap in the average density of eigenvalues of which is thus split into two pieces. When the spectrum of is tuned so that the gap closes, a new class of universality appears for the energy correlations in the vicinity of this singular point.
- Received 9 October 1997
DOI:https://doi.org/10.1103/PhysRevE.57.4140
©1998 American Physical Society