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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



An example of a periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum

Author: R. G. Shterenberg
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 2.
Journal: St. Petersburg Math. J. 16 (2005), 417-422
MSC (2000): Primary 35J10, 35P15
Published electronically: March 9, 2005
MathSciNet review: 2068347
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Abstract: The structure of the lower edge of the spectrum of a periodic magnetic Schrödinger operator is investigated. It is known that in the nonmagnetic case the energy depends quadratically on the quasimomentum in a neighborhood of the lower edge of the spectrum of the operator. An example of a magnetic Schrödinger operator is constructed for which energy is partially degenerate with respect to one component of the quasimomentum.

References [Enhancements On Off] (What's this?)

  • [BSu] Michael Birman and Tatyana Suslina, Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics, Systems, approximation, singular integral operators, and related topics (Bordeaux, 2000) Oper. Theory Adv. Appl., vol. 129, Birkhäuser, Basel, 2001, pp. 71–107. MR 1882692
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Additional Information

R. G. Shterenberg
Affiliation: St. Petersburg State University, Department of Physics, Petrodvorets, St. Petersburg 198504, Russia

Keywords: Periodic operator, magnetic Schr\"odinger operator, lower edge of the spectrum, threshold effects, degeneration
Received by editor(s): September 1, 2003
Published electronically: March 9, 2005
Additional Notes: Supported by RFBR (grant no. 02-01-00798).
Dedicated: Dedicated to my dear teacher M. Sh. Birman
Article copyright: © Copyright 2005 American Mathematical Society