This article is cited in 5 papers

On quantum averaging, quantum KAM, and quantum diffusion

S. B. Kuksin^ab, A. I. Neishtadt<sup>cd

a</sup> Steklov Mathematical Institute of the Russian Academy of Sciences
^b Institut de Mathématiques de Jussieu, Paris, France
^c Loughborough University, UK
^d Space Research Institute, Russian Academy of Sciences

Abstract: For non-autonomous Hamiltonian systems and their quantizations this paper discusses properties of the quantized systems whose classical analogues constitute the subject of KAM theory and related areas: averaging theory, Nekhoroshev stability, and diffusion.
Bibliography: 31 titles.

Keywords: infinite-dimensional KAM theory, quantum diffusion, quantum adiabatic theorem.

UDC: 517.956.8+517.958+530.145

MSC: 34C29, 81Q15

Received: 15.09.2012

DOI: 10.4213/rm9514

 English version: Russian Mathematical Surveys, 2013, 68:2, 335–348

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