On Schroedinger operators with dynamically defined potentials
Michael Goldstein, Wilhelm Schlag
TL;DR
This paper reviews recent research on Schrödinger operators with potentials defined by dynamical systems, focusing on properties of the integrated density of states and eigenvalue separation.
Contribution
It summarizes recent advances in understanding the spectral properties of these operators, especially regarding the IDS and eigenvalue separation.
Findings
Analysis of the fine structure of the IDS
Quantitative separation of Dirichlet eigenvalues
Insights into spectral properties of dynamically defined potentials
Abstract
We review some of the work by the authors on this topic. In particular, we discuss the recent paper "Fine properties of the IDS and a quantitative separation property of the Dirichlet eigenvalues".
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum chaos and dynamical systems · Matrix Theory and Algorithms