Homogeneous Spectrum of Quasi-periodic Gevrey Schr\"odinger Operators with Diophantine Frequency

TL;DR

This paper proves that for a class of quasi-periodic Schr"odinger operators with Gevrey potentials and Diophantine frequencies, a large coupling number ensures the spectrum is homogeneous, advancing understanding of spectral properties.

Contribution

It establishes the homogeneity of the spectrum for Gevrey Schr"odinger operators with Diophantine frequency under large coupling, a novel result in spectral theory.

Findings

Spectrum is homogeneous for large coupling

Results apply to Gevrey potentials with Diophantine frequencies

Advances understanding of spectral regularity in quasi-periodic operators

Abstract

We consider the quasi-periodic Schr\"odinger operator with the non-degenerate Gevrey potential for the Diophantine frequency. We prove that if the coupling number of the potential is large, then the spectrum is homogeneous.