02-229 F. Klopp and S. Nakamura
Anderson localization for 2D discrete Schr{\"o}dinger operator with random vector potential (285K, PDF) May 21, 02
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Abstract. We prove the Anderson localization near the bottom of the spectrum for two dimensional discrete Schr{\"o}dinger operators with a class of random vector potentials and no scalar potentials. Main lemmas are the Lifshitz tail and the Wegner estimate on the integrated density of states. Then, the Anderson localization, i.e., the pure point spectrum with exponentially decreasing eigenfunctions, is proved by the standard multiscale argument.

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