Effects of a Magnetic Field on the Trace of the Heat Kernel for a Schrödinger Operator with a Potential Well

Author: Odencrantz, Kristiana

Year: 1987

Degree: Dissertation (Ph.D.)

Advisor: Simon, Barry M.

Committee Members: Simon, Barry M.; Taylor, Michael E.; Anderson, Michael Thomas; Luxemburg, W. A. J.

Option: Mathematics

DOI: 10.7907/vd33-hs32

Abstract

This paper looks at the effect of a uniform magnetic field on the trace of the heat kernel for a Schrodinger operator with a well type potential. Using weighted Sobolev space techniques and noticing the gauge invariance of the perturbation, I show that the magnetic field first appears at a higher term in the small time asymptotic expansion of the trace of the heat kernel than might be naively expected.

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