Universality in quantum parametric correlations

TL;DR

This paper explores the universal behavior of quantum correlations in chaotic and disordered systems under parameter changes, introducing a reparametrization-invariant scaling method and applying it to eigenvalue curvature distributions.

Contribution

It presents a new universal scaling procedure for quantum correlation functions that is reparametrization-invariant and uniquely defined under broad conditions.

Findings

Introduces a general scaling method for quantum correlations.

Derives a semiclassical formula for the non-universal scaling factor.

Provides explicit expressions for billiard system deformations.

Abstract

We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations. Under certain general conditions we show that this procedure is unique. The approach is illustrated with the particular case of the distribution of eigenvalue curvatures. We also derive a semiclassical formula for the non-universal scaling factor, and give an explicit expression valid for arbitrary deformations of a billiard system.