Exponential Dynamical Localization for Random Word Models
Mathematical Physics
2021-07-09 v2 math.MP
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.
Keywords
Cite
@article{arxiv.1910.10214,
title = {Exponential Dynamical Localization for Random Word Models},
author = {Nishant Rangamani},
journal= {arXiv preprint arXiv:1910.10214},
year = {2021}
}