Gaussian ensembles distributions from mixing quantum systems

TL;DR

This paper derives Gaussian ensemble distributions from mixing quantum systems with classical analogs, linking quantum decoherence and random matrix theory in chaotic regimes.

Contribution

It introduces a derivation of Gaussian ensembles from mixing quantum systems and explores their connection to quantum chaos and decoherence.

Findings

Mixing quantum systems satisfy a factorization property for quantum mean values.

In the chaotic regime of the kicked rotator, decoherence relates to Gaussian ensembles.

The work connects random matrix theory with quantum chaotic systems through mixing properties.

Abstract

In the context of the mixing dynamical systems we present a derivation of the Gaussian ensembles distributions from mixing quantum systems having a classical analog that is mixing. We find that mixing factorization property is satisfied for the mixing quantum systems expressed as a factorization of quantum mean values. For the case of the kicked rotator and in its fully chaotic regime, the factorization property links decoherence by dephasing with Gaussian ensembles in terms of the weak limit, interpreted as a decohered state. Moreover, a discussion about the connection between random matrix theory and quantum chaotic systems, based on some attempts made in previous works and from the viewpoint of the mixing quantum systems, is presented.