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arXiv · 1901.05699

Trace formula for the magnetic Laplacian

Yuri A. Kordyukov·Iskander A. Taimanov
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Abstract

The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and 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. In this paper, we give a survey of basic notions and results related with the Guillemin-Uribe trace formula and provide concrete examples of its computation for two-dimensional constant curvature surfaces with constant magnetic fields and for the Katok example.

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Yuri A. Kordyukov, Iskander A. Taimanov. 2019-04-09. Trace formula for the magnetic Laplacian. https://doi.org/10.1070/rm9870

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