Interval spectrum for electric quantum walk and related skew-shift CMV matrices

TL;DR

This paper investigates the spectral properties of electric quantum walks and related CMV matrices, demonstrating that their spectra are the unit circle under certain irrational conditions and extending results to higher dimensions.

Contribution

It establishes the spectral characterization of quantum walks with electric fields and extends the analysis to CMV matrices with skew-shifts on higher-dimensional tori.

Findings

Spectrum is the unit circle for irrational electric fields.

Results apply to associated CMV matrices defined by skew-shifts.

Generalizations to higher-dimensional tori are achieved.

Abstract

We show that for a family of quantum walk models with electric fields, the spectrum is the unit circle for any irrational field. The result also holds for the associated CMV matrices defined by skew-shifts. Generalizations to CMV matrices with skew-shifts on higher dimensional torus are also obtained.