Parametric Level Correlations in Random-Matrix Models

TL;DR

This paper investigates parametric level correlations in random-matrix models, linking them to symmetry breaking between Green's functions, and provides a way to estimate the strength of level mixing due to parameter changes.

Contribution

It establishes a connection between parametric level correlations and symmetry breaking in random-matrix theories, extending previous disordered case results.

Findings

Correlation function form matches disordered case

Strength factor depends on Goldstone mode

Number of strongly mixed levels can be estimated

Abstract

We show that parametric level correlations in random-matrix theories are closely related to a breaking of the symmetry between the advanced and the retarded Green's functions. The form of the parametric level correlation function is the same as for the disordered case considered earlier by Simons and Altshuler and is given by the graded trace of the commutator of the saddle--point solution with the particular matrix that describes the symmetry breaking in the actual case of interest. The strength factor differs from the case of disorder. It is determined solely by the Goldstone mode. It is essentially given by the number of levels that are strongly mixed as the external parameter changes. The factor can easily be estimated in applications.