On quantum averaging, quantum KAM and quantum diffusion

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.

15 pages

References in corpus (1)

• KAM for the quantum harmonic oscillator

Cited by in corpus (2)

• Rational solutions of the Sasano system of type $D_5^{(1)}$
• Robustness of quantum symmetries against perturbations