Random-Matrix Theory of Parametric Correlations in the Spectra of Disordered Metals and Chaotic Billiards

TL;DR

This paper applies random-matrix theory to analyze how external perturbations affect the energy spectra of disordered metals and chaotic billiards, confirming that spectral correlations depend mainly on symmetry and level repulsion.

Contribution

It demonstrates that Dyson's Brownian-motion model accurately reproduces microscopic results, validating the dominance of level repulsion in parametric spectral correlations.

Findings

Dyson's model matches microscopic theory results.

Parametric correlations depend primarily on Hamiltonian symmetry.

Level repulsion governs spectral response to perturbations.

Abstract

We study the response to an external perturbation of the energy levels of a disordered metallic particle, by means of the Brownian-motion model introduced by Dyson in the theory of random matrices, and reproduce the results of a recent microscopic theory of Altshuler, Simons, and Szafer. This establishes the validity of Dyson's basic assumption, that parametric correlations in the energy spectrum are dominated by level repulsion, and therefore solely dependent on the symmetry of the hamiltonian. ***Submitted to Physica A.****