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St. Petersburg Mathematical Journal
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 | References | Similar Articles | Additional Information

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?)

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Additional Information

R. G. Shterenberg
Affiliation: St. Petersburg State University, Department of Physics, Petrodvorets, St. Petersburg 198504, Russia
Email: roman@RS3759.spb.edu

DOI: http://dx.doi.org/10.1090/S1061-0022-05-00858-7
PII: S 1061-0022(05)00858-7
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