Parametric Number Covariance in Quantum Chaotic Spectra

TL;DR

This paper introduces the number covariance as a new measure of spectral parametric correlations in quantum chaotic systems, deriving universal analytic results for random matrix ensembles and illustrating them with quantum kicked rotor examples.

Contribution

It presents the first analytic derivation of number covariance in quantum chaotic spectra and demonstrates its universality across different systems.

Findings

Analytic expressions for number covariance in classical random matrix ensembles.

Universality of the number covariance across different quantum chaotic systems.

Application to quantum kicked rotors confirming theoretical predictions.

Abstract

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the co- variance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal non-invariant cases. A local version of the parametric number variance introduced earlier is also investigated.