Parametric number covariance in quantum chaotic spectra

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 covariance. 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 noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

Quantum Chaotic Systems and Random Matrix Theory

“…We consider N = 1000. Since the spectra in the highly chaotic case (α very large) are known to become independent [48] very rapidly with increasing α, we generate spectra for α ranging from 10 4 to 10 6 , in steps of 1000. This gives us 1000 independent spectra.…”