Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators.
In: Transactions of the American Mathematical Society, Jg. 353 (2001-02-01), Heft 2, S. 635-653
Online
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Zugriff:
We prove exponential localization at all energies for two types of one-dimen\-sional random Schrödinger operators: the Poisson model and the random displacement model. As opposed to Anderson-type models, these operators are not monotonic in the random parameters. Therefore the classical one-parameter version of spectral averaging, as used in localization proofs for Anderson models, breaks down. We use the new method of two-parameter spectral averaging and apply it to the Poisson as well as the displacement case. In addition, we apply results from inverse spectral theory, which show that two-parameter spectral averaging works for sufficiently many energies (all but a discrete set) to conclude localization at all energies. [ABSTRACT FROM AUTHOR]
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Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators.
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Autor/in / Beteiligte Person: | Buschmann, Dirk ; Stolz, Günter |
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Zeitschrift: | Transactions of the American Mathematical Society, Jg. 353 (2001-02-01), Heft 2, S. 635-653 |
Veröffentlichung: | 2001 |
Medientyp: | academicJournal |
ISSN: | 0002-9947 (print) |
DOI: | 10.1090/S0002-9947-00-02674-X |
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