ISSN:
1572-9613
Keywords:
random Schrödinger operators
;
Anderson localization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum particle in multi-dimensional Euclidean space under the influence of suitable random potentials has almost surely a pure-point component. The result applies in particular to a certain class of zero-mean 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 fixed-energy multi-scale analysis which allows for different random potentials on different length scales.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1026425621261
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