An example of a periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum
HTML articles powered by AMS MathViewer
- by
R. G. Shterenberg
Translated by: the author - St. Petersburg Math. J. 16 (2005), 417-422
- DOI: https://doi.org/10.1090/S1061-0022-05-00858-7
- Published electronically: March 9, 2005
- PDF | Request permission
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
- 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
- Michael Reed and Barry Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 0493421
- M. M. Skriganov, Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators, Trudy Mat. Inst. Steklov. 171 (1985), 122 (Russian). MR 798454
Bibliographic Information
- R. G. Shterenberg
- Affiliation: St. Petersburg State University, Department of Physics, Petrodvorets, St. Petersburg 198504, Russia
- Email: roman@RS3759.spb.edu
- Received by editor(s): September 1, 2003
- Published electronically: March 9, 2005
- Additional Notes: Supported by RFBR (grant no. 02-01-00798).
- © Copyright 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 417-422
- MSC (2000): Primary 35J10, 35P15
- DOI: https://doi.org/10.1090/S1061-0022-05-00858-7
- MathSciNet review: 2068347
Dedicated: Dedicated to my dear teacher M. Sh. Birman