Fractional Moment Methods for Anderson Localization in the Continuum

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dc.creatorAizenman, Michael
dc.creatorElgart, Alexander
dc.creatorNaboko, Sergey
dc.creatorSchenker, Jeffrey H.
dc.creatorStolz, Günter
dc.date2003-09-05
dc.date.accessioned2026-07-07T04:30:32Z
dc.date.available2026-07-07T04:30:32Z
dc.descriptionThe fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schrödinger operators in the continuum. One of the new results for continuum operators are exponentially decaying bounds for the mean value of transition amplitudes, for energies throughout the localization regime. An obstacle which up to now prevented an extension of this method to the continuum is the lack of a uniform bound on the Lifshitz-Krein spectral shift associated with the local potential terms. This difficulty is resolved through an analysis of the resonance-diffusing effects of the disorder.
dc.descriptionThis is a brief announcement of math-ph/0308023, written for the proceedings of ICMP 2003
dc.identifierhttps://arxiv.org/abs/math-ph/0309018
dc.identifierhttp://arxiv.org/abs/math-ph/0309018
dc.identifierProceedings, Int. Cong. Math. Phys. (Lisbon 2003), (World Scientific, 2003).
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57494
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject82B44; 46N50
dc.titleFractional Moment Methods for Anderson Localization in the Continuum
dc.typetext

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