Schr\"odinger Operators with Dynamically Defined Potentials: A Survey
Spectral Theory
2019-02-25 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schr\"odinger operators whose potentials are obtained by real-valued sampling along the orbits of an ergodic invertible transformation. After an introductory part explaining basic spectral concepts and fundamental results, we present the general theory of such operators, and then provide an overview of known results for specific classes of potentials. Here we focus primarily on the cases of random and almost periodic potentials.
Cite
@article{arxiv.1410.2445,
title = {Schr\"odinger Operators with Dynamically Defined Potentials: A Survey},
author = {David Damanik},
journal= {arXiv preprint arXiv:1410.2445},
year = {2019}
}
Comments
81 pages, to appear in Ergodic Theory Dynam. Systems