Trace formula for the magnetic Laplacian Full article
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Russian Mathematical Surveys
ISSN: 0036-0279 , E-ISSN: 1468-4829 |
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| Output data | Year: 2019, Volume: 74, Number: 2, Pages: 325-361 Pages count : 37 DOI: 10.1070/RM9870 | ||||||
| Tags | magnetic geodesics; magnetic Laplacian; trace formula | ||||||
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Abstract:
The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and the more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds, which reflects the dynamics of magnetic geodesic flows in terms of eigenvalues of a natural differential operator (the magnetic Laplacian) associated with the magnetic field. This paper gives a survey of basic notions and results related to the Guillemin-Uribe trace formula and provides concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example.
Cite:
Kordyukov Y.A.
, Taimanov I.A.
Trace formula for the magnetic Laplacian
Russian Mathematical Surveys. 2019. V.74. N2. P.325-361. DOI: 10.1070/RM9870 WOS Scopus OpenAlex
Trace formula for the magnetic Laplacian
Russian Mathematical Surveys. 2019. V.74. N2. P.325-361. DOI: 10.1070/RM9870 WOS Scopus OpenAlex
Original:
Кордюков Ю.А.
, Тайманов И.А.
Формула следа для магнитного лапласиана
Успехи математических наук. 2019. Т.74. №2. С.149-186. DOI: 10.4213/rm9870 РИНЦ OpenAlex
Формула следа для магнитного лапласиана
Успехи математических наук. 2019. Т.74. №2. С.149-186. DOI: 10.4213/rm9870 РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000474710200004 |
| Scopus: | 2-s2.0-85072728453 |
| OpenAlex: | W2908991848 |