Journals Information
Universal Journal of Applied Mathematics Vol. 3(4), pp. 63 - 76
DOI: 10.13189/ujam.2015.030401
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Exponential Dynamical Anderson Localization in N-particle Models on Graphs with Infinite-range Interaction
Victor Chulaevsky *
Department of Mathematics, University of Reims Champagne-Ardenne, France
ABSTRACT
We extend the techniques and results of the multi-particle variant of the Fractional Moment Method, developed by Aizenman and Warzel, to disordered quantum systems in general finite or countable graphs with polynomial growth of balls, in presence of an exponentially decaying interaction. In the strong disorder regime, we prove complete exponential multi-particle strong localization. Prior results, obtained with the help of the multi-scale analysis, proved only a sub-exponential decay of eigenfunction correlators.
KEYWORDS
Multi-particle Anderson Localization, Eigenvalue Concentration Estimates.
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Victor Chulaevsky , "Exponential Dynamical Anderson Localization in N-particle Models on Graphs with Infinite-range Interaction," Universal Journal of Applied Mathematics, Vol. 3, No. 4, pp. 63 - 76, 2015. DOI: 10.13189/ujam.2015.030401.
(b). APA Format:
Victor Chulaevsky (2015). Exponential Dynamical Anderson Localization in N-particle Models on Graphs with Infinite-range Interaction. Universal Journal of Applied Mathematics, 3(4), 63 - 76. DOI: 10.13189/ujam.2015.030401.