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Non-monotonic Random Schrödinger Operators: The Anderson Model

✍ Scribed by Günter Stolz

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
105 KB
Volume
248
Category
Article
ISSN
0022-247X

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✦ Synopsis

We prove exponential localization at all energies for one-dimensional continuous Anderson-type models with single site potentials of changing sign. A periodic background potential is allowed. The main problem arises from non-monotonicity; i.e., the operator does not depend monotonically in the form sense on the random parameters. We show that the method of ''two-parameter spectral averaging,'' recently devised by Buschmann and Stolz to prove localization for Poisson and random displacement models, can be modified to work for the type of Anderson model considered here.

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