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Schrödinger operators with dynamically defined potentials

Published online by Cambridge University Press:  11 February 2016

DAVID DAMANIK
DAVID DAMANIK*
Affiliation:
Department of Mathematics, Rice University, Houston, TX 77005, USA email [email protected]
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Abstract

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In this survey we discuss spectral and quantum dynamical properties of discrete one-dimensional Schrödinger 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.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 6 , September 2017 , pp. 1681 - 1764
Copyright
© Cambridge University Press, 2016 

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