Quantum chaos and its kinetic stage of evolution

TL;DR

This paper investigates the emergence of irreversibility in small open quantum systems, emphasizing the role of complex energy spectrum structures, especially in chaotic systems with few degrees of freedom, using the Mathieu-Schrodinger equation as a case study.

Contribution

It demonstrates that the complex structure of the energy spectrum is crucial for irreversibility in chaotic quantum systems with few degrees of freedom, challenging traditional views.

Findings

Irreversibility is linked to the energy spectrum's complex structure.

Chaotic quantum systems exhibit non-trivial spectral domains.

Spectrum features degenerated and non-degenerated states separated by branch points.

Abstract

Usually reason of irreversibility in open quantum-mechanical system is interaction with a thermal bath, consisting form infinite number of degrees of freedom. Irreversibility in the system appears due to the averaging over all possible realizations of the environment states. But, in case of open quantum-mechanical system with few degrees of freedom situation is much more complicated. Should one still expect irreversibility, if external perturbation is just an adiabatic force without any random features? Problem is not clear yet. This is main question we address in this review paper. We prove that key point in the formation of irreversibility in chaotic quantum-mechanical systems with few degrees of freedom, is the complicated structure of energy spectrum. We shall consider quantum mechanical-system with parametrically dependent energy spectrum. In particular, we study energy spectrum of the Mathieu-Schrodinger equation. Structure of the spectrum is quite non-trivial, consists from the domains of non-degenerated and degenerated stats, separated from each other by branch points.