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Direct Scaling Analysis of Localization in Single-Particle Quantum Systems on Graphs with Diagonal Disorder

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Abstract

We propose a simplified version of the Multi-Scale Analysis of Anderson models on a lattice and, more generally, on a countable graph with polynomially bounded growth of balls, with diagonal disorder represented by an IID or strongly mixing correlated potential. We apply the new scaling procedure to discrete Schrödinger operators and obtain localization bounds on eigenfunctions and eigenfunction correlators in arbitrarily large finite subsets of the graph which imply the spectral and strong dynamical localization in the entire graph.

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  1. Département de Mathématiques, Université de Reims, Moulin de la Housse, B.P. 1039, 51687, Reims Cedex 2, France

    Victor Chulaevsky

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  1. Victor Chulaevsky
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Correspondence to Victor Chulaevsky.

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Chulaevsky, V. Direct Scaling Analysis of Localization in Single-Particle Quantum Systems on Graphs with Diagonal Disorder. Math Phys Anal Geom 15, 361–399 (2012). https://doi.org/10.1007/s11040-012-9116-8

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  • DOI: https://doi.org/10.1007/s11040-012-9116-8

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