 00414 Werner Fischer, Hajo Leschke, Peter Mueller
 Spectral Localization by Gaussian Random Potentials
in MultiDimensional Continuous Space
(489K, Postscript)
Oct 23, 00

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Abstract. A detailed mathematical proof is given that the energy spectrum of a
nonrelativistic quantum particle
in multidimensional Euclidean space under the influence of
suitable random potentials has almost surely a purepoint component.
The result applies in particular to a certain class of zeromean
Gaussian random potentials, which are homogeneous with respect to
Euclidean translations. More precisely, for these Gaussian random
potentials the spectrum is almost surely only pure point at
sufficiently negative energies or, at negative energies, for
sufficiently weak disorder.
The proof is based on a fixedenergy multiscale
analysis which allows for different random potentials on different
length scales.
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