On the Spectrum of Multi-Frequency Quasiperiodic Schr\"odinger Operators with Large Coupling
Spectral Theory
2017-09-01 v1 Mathematical Physics
math.MP
Abstract
We study multi-frequency quasiperiodic Schr\"{o}dinger operators on . We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of a criterion for the spectrum to contain an interval at a given location that we establish non-perturbatively in the regime of positive Lyapunov exponent.
Keywords
Cite
@article{arxiv.1708.09711,
title = {On the Spectrum of Multi-Frequency Quasiperiodic Schr\"odinger Operators with Large Coupling},
author = {Michael Goldstein and Wilhelm Schlag and Mircea Voda},
journal= {arXiv preprint arXiv:1708.09711},
year = {2017}
}