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arXiv · 1910.10214

Exponential Dynamical Localization for Random Word Models

Nishant Rangamani
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Abstract

We show that one-dimensional Schr{\"o}dinger operators whose potentials arise by randomly concatenating words from an underlying set exhibit exponential dynamical localization (EDL) on any compact set which trivially intersects a finite set of critical energies. We do so by first giving a new proof of spectral localization for such operators and then showing that once one has the existence of a complete orthonormal basis of eigenfunctions (with probability one), the same estimates used to prove it naturally lead to a proof of the aforementioned EDL result. The EDL statements provide new localization results for several classes of random Schr{\"o}dinger operators including random polymer models and generalized Anderson models.

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Nishant Rangamani. 2019-10-22. Exponential Dynamical Localization for Random Word Models. https://arxiv.org/abs/1910.10214

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