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This article is cited in 8 scientific papers (total in 9 papers)
Trace formula for the magnetic Laplacian
Yu. A. Kordyukovab, I. A. Taimanovcb a Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa
b Novosibirsk State University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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.
Bibliography: 53 titles.
Keywords:
trace formula, magnetic Laplacian, magnetic geodesics.
Received: 28.12.2018
Citation:
Yu. A. Kordyukov, I. A. Taimanov, “Trace formula for the magnetic Laplacian”, Uspekhi Mat. Nauk, 74:2(446) (2019), 149–186; Russian Math. Surveys, 74:2 (2019), 325–361
Linking options:
https://www.mathnet.ru/eng/rm9870https://doi.org/10.1070/RM9870 https://www.mathnet.ru/eng/rm/v74/i2/p149
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Abstract page: | 726 | Russian version PDF: | 110 | English version PDF: | 46 | References: | 72 | First page: | 81 |
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