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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Semiclassical asymptotics and gaps in the spectra of periodic Schrödinger operators with magnetic wells
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by Bernard Helffer and Yuri A. Kordyukov PDF
Trans. Amer. Math. Soc. 360 (2008), 1681-1694 Request permission


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
  • MR Author ID: 83860
  • Email:
  • Yuri A. Kordyukov
  • Affiliation: Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky str., 450077 Ufa, Russia
  • MR Author ID: 227886
  • ORCID: 0000-0003-2957-2873
  • Email:
  • 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).
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 1681-1694
  • MSC (2000): Primary 35P20, 35J10, 47F05, 81Q10
  • DOI:
  • MathSciNet review: 2357710