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ISSN 1088-6850(e) ISSN 0002-9947(p)

Semiclassical asymptotics and gaps in the spectra of periodic Schrödinger operators with magnetic wells

Author(s): Bernard Helffer; Yuri A. Kordyukov
Journal: Trans. Amer. Math. Soc. 360 (2008), 1681-1694.
MSC (2000): Primary 35P20, 35J10, 47F05, 81Q10
Posted: September 25, 2007
MathSciNet review: 2357710
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Abstract | References | Similar articles | Additional information

Abstract: We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schrödinger operator with magnetic wells on a noncompact Riemannian manifold such that $H^1(M, \mathbb{R})=0$ , equipped with a properly disconnected, cocompact action of a finitely generated, discrete group of isometries, has an arbitrarily large number of spectral gaps in the semi-classical limit.

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Additional Information:

Bernard Helffer
Affiliation: Département de Mathématiques, Bâtiment 425, F91405 Orsay Cédex, France
Email: Bernard.Helffer@math.u-psud.fr

Yuri A. Kordyukov
Affiliation: Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky str., 450077 Ufa, Russia
Email: yurikor@matem.anrb.ru

DOI: 10.1090/S0002-9947-07-04423-6
PII: S 0002-9947(07)04423-6
Received by editor(s): December 21, 2005
Received by editor(s) in revised form: September 12, 2006
Posted: September 25, 2007
Additional Notes: The first author acknowledges support from the SPECT programme of the ESF and from the European Research Network `Postdoctoral Training Program in Mathematical Analysis of Large Quantum Systems' with contract number HPRN-CT-2002-00277.
The second author acknowledges support from the Russian Foundation of Basic Research (grant no. 04-01-00190).
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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