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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 Z\mathbb{Z} . 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}
}