03-78 Dirk Hundertmark, Barry Simon

A Diamagnetic Inequality for Semigroup Differences (94K, LaTeX2e) Mar 1, 03

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Abstract. The diamagnetic inequality for the magnetic Schr\"odinger semigroup is extended to the difference of the semigroups of magnetic Schr\"odinger operators with Neumann and Dirichlet boundary conditions on arbitrary open domains and rather general magnetic vector potentials $A$ and potentials $V$. In particular, this bound renders moot all the technical issues in the recent proofs of the independence of the boundary conditions for the integrated density of states for magnetic Schr\"odinger operators: Independence of the boundary conditions for the free case, that is, for vanishing potentials and vector potentials, immediately implies independence of the boundary conditions of the integrated density of states for a large class of magnetic Schr\"odinger operators.

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