Large time behavior of the heat kernel of two-dimensional magnetic Schroedinger operators
Mathematical Physics
2011-07-19 v1 math.MP
Spectral Theory
Abstract
We study the heat semigroup generated by two-dimensional Schroedinger operators with compactly supported magnetic field. We show that if the field is radial, then the large time behavior of the associated heat kernel is determined by its total flux. We also establish some on-diagonal heat kernel estimates and discuss their applications for solutions to the heat equation. An exact formula for the heat kernel, and for its large time asymptotic, is derived in the case of the Aharonov-Bohm magnetic field.
Keywords
Cite
@article{arxiv.1007.1851,
title = {Large time behavior of the heat kernel of two-dimensional magnetic Schroedinger operators},
author = {Hynek Kovarik},
journal= {arXiv preprint arXiv:1007.1851},
year = {2011}
}