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Uspekhi Mat. Nauk, 2013, Volume 68, Issue 2(410), Pages 145–158 (Mi umn9514)  

This article is cited in 2 scientific papers (total in 2 papers)

On quantum averaging, quantum KAM, and quantum diffusion

S. B. Kuksinab, A. I. Neishtadtcd

a 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.

Funding Agency Grant Number
Agence Nationale de la Recherche ANR-10-BLAN 0102
Russian Foundation for Basic Research 13-01-00251


DOI: https://doi.org/10.4213/rm9514

Full text: PDF file (628 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.956.8+517.958+530.145
MSC: 34C29, 81Q15
Received: 15.09.2012

Citation: S. B. Kuksin, A. I. Neishtadt, “On quantum averaging, quantum KAM, and quantum diffusion”, Uspekhi Mat. Nauk, 68:2(410) (2013), 145–158; Russian Math. Surveys, 68:2 (2013), 335–348

Citation in format AMSBIB
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\pages 145--158
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Fontanari D. Fasso F. Sadovskii D.A., “Quantum manifestations of Nekhoroshev stability”, Phys. Lett. A, 380:39 (2016), 3167–3172  crossref  isi  elib  scopus
    2. Treschev D.V., Zubelevich O.E., “On a Heavy Quantum Particle”, Russ. J. Math. Phys., 26:1 (2019), 109–121  crossref  mathscinet  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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