Fractional moment methods for Anderson localization in the continuum

Günter Stolz, Michael Aizenman, Alexander Elgart, Sergey Naboko, Jeffrey H. Schenker

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The 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 Schrodinger 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.

Original languageEnglish (US)
Title of host publicationXIVth International Congress on Mathematical Physics
Subtitle of host publicationLisbon, 28 July - 2 August 2003
PublisherWorld Scientific Publishing Co.
Pages619-625
Number of pages7
ISBN (Electronic)9789812704016
ISBN (Print)981256201X, 9789812562012
DOIs
StatePublished - Jan 1 2006

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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