95-195 Knill O.

Discrete random electromagnetic Laplacians (103K, LaTeX) Apr 12, 95

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Abstract. We consider discrete random magnetic Laplacians in the plane and discrete random electromagnetic Laplacians in higher dimensions. The existence of these objects relies on a theorem of Feldman-Moore which was generalized by Lind to the nonabelian case. For example, it allows to realize ergodic Schr\"odinger operators with stationary independent magnetic fields on discrete two dimensional lattices including also nonperiodic situations like Penrose lattices. The theorem is generalized here to higher dimensions. The Laplacians obtained from the electromagnetic vector potential are elements of a von Neumann algebra constructed from the underlying dynamical system respectively from the ergodic equivalence relation. They generalize Harper operators which correspond to constant magnetic fields. For independent identically distributed magnetic fields and special Anderson models, we compute the density of states using a random walk expansion.

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