Moment Analysis for Localization in Random Schroedinger Operators

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dc.creatorAizenman, Michael
dc.creatorElgart, Alexander
dc.creatorNaboko, Serguei
dc.creatorSchenker, Jeffrey H.
dc.creatorStolz, Gunter
dc.date2003-08-20
dc.date2005-11-03
dc.date.accessioned2026-07-07T10:05:31Z
dc.date.available2026-07-07T10:05:31Z
dc.descriptionWe study localization effects of disorder on the spectral and dynamical properties of Schroedinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are finite due to the resonance-diffusing effects of the disorder. The main difficulty which has up to now prevented an extension of this method to the continuum can be traced to the lack of a uniform bound on the Lifshitz-Krein spectral shift associated with the local potential terms. The difficulty is avoided here through the use of a weak-L1 estimate concerning the boundary-value distribution of resolvents of maximally dissipative operators, combined with standard tools of relative compactness theory.
dc.descriptionLatex file, 63 pp; v2. introduction rewritten and other sections revised to streamline and clarify presentation; v3. a number of typos corrected
dc.identifierhttps://arxiv.org/abs/math-ph/0308023
dc.identifierhttp://arxiv.org/abs/math-ph/0308023
dc.identifierInventiones Mathematicae, v. 163, p. 343 (2006).
dc.identifierdoi:10.1007/s00222-005-0463-y
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170032
dc.subjectMathematical Physics
dc.subjectDisordered Systems and Neural Networks
dc.subjectSpectral Theory
dc.subject82B44; 46N50
dc.titleMoment Analysis for Localization in Random Schroedinger Operators
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