- 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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