Inserted: 9 jul 2010
Last Updated: 5 may 2012
Journal: Calc. Var. Partial Differential Equations
We study the heat semigroup generated by two-dimensional Schrödinger 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. An exact formula for the heat kernel, and for its large time asymptotic, is derived in the case of the Aharonov-Bohm magnetic field. We also establish some on-diagonal heat kernel estimates and discuss their applications for solutions to the heat equation.
Keywords: Heat kernel, magnetic field, Schrödinger operator, Pauli operator