A note on fractional moments for the one-dimensional continuum Anderson model

Eman Hamza; Robert Sims; Günter Stolz

doi:10.1016/j.jmaa.2009.11.005

A note on fractional moments for the one-dimensional continuum Anderson model

Eman Hamza, Robert Sims, Günter Stolz

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9 Scopus citations

Abstract

We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supported density.

Original language	English (US)
Pages (from-to)	435-446
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	365
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2009.11.005
State	Published - May 15 2010

Keywords

Anderson localization
Anderson model
Fractional moments method

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2009.11.005

Cite this

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title = "A note on fractional moments for the one-dimensional continuum Anderson model",

abstract = "We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supported density.",

keywords = "Anderson localization, Anderson model, Fractional moments method",

author = "Eman Hamza and Robert Sims and G{\"u}nter Stolz",

year = "2010",

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T1 - A note on fractional moments for the one-dimensional continuum Anderson model

AU - Hamza, Eman

AU - Sims, Robert

AU - Stolz, Günter

PY - 2010/5/15

Y1 - 2010/5/15

N2 - We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supported density.

AB - We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supported density.

KW - Anderson localization

KW - Anderson model

KW - Fractional moments method

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DO - 10.1016/j.jmaa.2009.11.005

M3 - Article

AN - SCOPUS:74849135432

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VL - 365

SP - 435

EP - 446

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A note on fractional moments for the one-dimensional continuum Anderson model

Abstract

Keywords

ASJC Scopus subject areas

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