Hynek Kovarik – Large time behavior of the heat kernel of two-dimensional magnetic Schroedinger operators.

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Date(s) - 23 juin 2010

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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. An exact formula for the heat kernel, and for its large time asymptotic, is derived in the case of the Aharonov-Bohm operator. We also establish some on-diagonal heat kernel estimates and discuss their applications.