On the spectrum of skew-shift Schr\"odinger operators

TL;DR

This paper demonstrates that in the semi-classical regime, the spectrum of skew-shift Schr"odinger operators includes large intervals that tend to the potential's range, revealing spectral properties in this limit.

Contribution

The paper establishes the presence of large spectral intervals in skew-shift Schr"odinger operators in the semi-classical limit, connecting spectral features to the potential's range.

Findings

Large spectral intervals exist in the semi-classical regime.

Spectral intervals approach the potential's range as the semi-classical limit is approached.

Provides insight into spectral behavior of skew-shift Schr"odinger operators.

Abstract

I prove that the spectrum of a skew-shift Schr\"odinger operator contains larges interval in the semi-classical regime. In the semi-classical limit, these intervals approach the range of the potential.