## Pichard, in Quantum Coherence in Mesoscopic Systems (NATO

- PICH.J.-L
- ASI series,
- 1991

- Published 1993

We study the correlation between the energy spectra of two disordered Hamiltonians of the form Ha = H0a + saφ (a=1,2) with H0a and φ drawn from random distributions. We calculate this correlation function explicitly and show that it has a simple universal form for a broad class of random distributions. In a series of recent papers [BZ1, BZ2, BZ3] (hereafter to be referred to as I, II, and III respectively) we studied the theory of random matrices [WIG,POR,MEH] and discovered a remarkably simple universality in the correlation between energy eigenvalues of random Hamiltonians. A brief review and summary of our work may be found in III. In particular, we find that for a large class of Hamiltonians, the smoothed connected correlation (to be defined below) between the density of energy eigenvalues at energies μ and ν has the universal form ρsmooth c (μ, ν) = −1 2(Nπa)2 1 (x− y)2 { (1− xy) [(1− x2)(1− y2)]1/2 }

@inproceedings{Brzin1993arXI,
title={ar X iv : c on d - m at / 9 31 10 46 v 1 1 8 N ov 1 99 3 NSF - ITP - 93 - 136 Universal Spectral Correlation between Hamiltonians with Disorder},
author={E . Br{\'e}zin},
year={1993}
}