Geodesic
Trace formula for the magnetic Laplacian
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 2, pp. 325-361

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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: magnetic Laplacian, magnetic geodesics.
Mots-clés : trace formula 
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     title = {Trace formula for the magnetic {Laplacian}},
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Yu. A. Kordyukov; I. A. Taimanov. Trace formula for the magnetic Laplacian. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 2, pp. 325-361. http://geodesic.mathdoc.fr/item/RM_2019_74_2_a3/