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arXiv · 1906.05752

Anderson localisation in stationary ensembles of quasiperiodic operators

Victor Chulaevsky·Sasha Sodin
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Abstract

An ensemble of quasi-periodic discrete Schr\"{o}dinger operators with an arbitrary number of basic frequencies is considered, in a lattice of arbitrary dimension, in which the hull function is a realisation of a stationary Gaussian process on the torus. We show that, for almost every element of the ensemble, the quasi-periodic operator boasts Anderson localization with simple pure point spectrum at strong coupling. One of the ingredients of the proof is a new lower bound on the interpolation error for stationary Gaussian processes on the torus (also known as local non-determinism).

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Victor Chulaevsky, Sasha Sodin. 2019-06-13. Anderson localisation in stationary ensembles of quasiperiodic operators. https://arxiv.org/abs/1906.05752

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