Trace formula for the magnetic Laplacian

Autor:	Kordyukov, Yuri A., Taimanov, Iskander A.
Rok vydání:	2019
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Dynamical Systems Mathematics - Spectral Theory
Zdroj:	Russian Math. Surveys 74:2 (2019), 325-361
Druh dokumentu:	Working Paper
DOI:	10.1070/RM9870
Popis:	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. Comment: 37 pages, v2: minor corrections, references added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1901.05699 Zobrazit plný text záznamu View this record from Arxiv