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Russian Mathematical Surveys, 2019, Volume 74, Issue 2, Pages 325–361
DOI: https://doi.org/10.1070/RM9870 (Mi rm9870) 		 
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
English version PDF (694 kB) Citations (9)
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DOI: https://doi.org/10.1070/RM9870
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0025
This work was supported by the Laboratory of Topology and Dynamics at Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation).
Received: 28.12.2018
Russian version:
Uspekhi Matematicheskikh Nauk, 2019, Volume 74, Issue 2(446), Pages 149–186
DOI: https://doi.org/10.4213/rm9870
Bibliographic databases:
Document Type: Article
UDC: 517.984+514.774.8
MSC: Primary 58J50; Secondary 37J35, 58J37, 81Q20
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:110
    English version PDF:46
    References:72
    First page:81
     
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