Localization for the random displacement model

Abstract

We prove spectral and dynamical localization for the multi-dimensional random displacement model near the bottom of its spectrum by showing that the approach through multiscale analysis is applicable. In particular, we show that a previously known Lifshitz tail bound can be extended to our setting and prove a new Wegner estimate. A key tool is given by a quantitative form of a property of a related single-site Neumann problem which can be described as "bubbles tend to the corners".

Corrected typos and improved some arguments

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• Lifshitz tails for Schrödinger operators with random breather potential
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• Spectral geometry of flat tori with random impurities
• Spectral localization for quantum Hamiltonians with weak random delta interaction
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• Quantitative equidistribution of eigenfunctions for toral Schrödinger operators