Trace formula for the magnetic Laplacian
Differential Geometry
2022-08-30 v2 Mathematical Physics
Dynamical Systems
math.MP
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1901.05699,
title = {Trace formula for the magnetic Laplacian},
author = {Yuri A. Kordyukov and Iskander A. Taimanov},
journal= {arXiv preprint arXiv:1901.05699},
year = {2022}
}
Comments
37 pages, v2: minor corrections, references added