The Schrödinger operator is a fundamental model of a
single-particle Hamiltonian in quantum mechanics. We show how to prove
estimates on the size of the spectra of ergodic Schrödinger
operators using cocycle techniques and uniform hyperbolicity. In
particular, hyperbolicity across long blocks leads to exponentially
small upper bounds on the size of the spectrum in suitable energy
regions. We will review some of the relevant background.
Webmaster University of Houston
---
Last modified: April 08 2016 - 20:30:35