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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 261, Pages 176–187 (Mi tm747)  
This article is cited in 7 scientific papers (total in 7 papers)

Periodic Magnetic Schrödinger Operators: Spectral Gaps and Tunneling Effect

Yu. A. Kordyukova, B. Helfferb

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b Paris-Sud University 11
Full-text PDF (214 kB) Citations (7)
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Abstract: A periodic Schrödinger operator on a noncompact Riemannian manifold $M$ such that $H^1(M,\mathbb R)=0$ endowed with a properly discontinuous cocompact isometric action of a discrete group is considered. Under some additional conditions on the magnetic field, the existence of an arbitrary large number of gaps in the spectrum of such an operator in the semiclassical limit is established. The proofs are based on the study of the tunneling effect in the corresponding quantum system.
Received in July 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 261, Pages 171–182
DOI: https://doi.org/10.1134/S0081543808020132
Bibliographic databases:
UDC: 517.984
Language: Russian
Citation: Yu. A. Kordyukov, B. Helffer, “Periodic Magnetic Schrödinger Operators: Spectral Gaps and Tunneling Effect”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 176–187; Proc. Steklov Inst. Math., 261 (2008), 171–182
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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