On quantum averaging, quantum KAM and quantum diffusion

TL;DR

This paper explores the properties of quantised nonautonomous Hamiltonian systems, linking quantum behaviors to classical KAM-related theories such as averaging, stability, and diffusion, to understand quantum dynamics better.

Contribution

It provides a theoretical analysis connecting quantum properties with classical KAM-related theories for nonautonomous Hamiltonian systems.

Findings

Quantum systems exhibit properties analogous to classical KAM theory.

Averaging and Nekhoroshev stability concepts extend to quantum systems.

Quantum diffusion behaviors are analyzed in relation to classical dynamics.

Abstract

For nonautonomous Hamiltonian systems and their quantisations we discuss properties of the quantised systems, related to those of the corresponding classical systems, described by the KAM-related theories: the proper KAM, the averaging theory, the Nekhoroshev stability and the diffusion.