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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Authors: Bernard Helffer and Yuri A. Kordyukov
Journal: Trans. Amer. Math. Soc. 360 (2008), 1681-1694
MSC (2000): Primary 35P20, 35J10, 47F05, 81Q10
DOI: https://doi.org/10.1090/S0002-9947-07-04423-6
Published electronically: September 25, 2007
MathSciNet review: 2357710
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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 $ M$ 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: https://doi.org/10.1090/S0002-9947-07-04423-6
Received by editor(s): December 21, 2005
Received by editor(s) in revised form: September 12, 2006
Published electronically: 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).
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.