On absolutely continuous spectrum for one-channel unitary operators

TL;DR

This paper introduces a new formalism for analyzing the spectral properties of one-channel unitary operators, extending existing methods and providing criteria for absolutely continuous spectrum, especially in the context of random perturbations.

Contribution

It develops a radial transfer matrix formalism for unitary operators, generalizing prior models and establishing criteria for absolutely continuous spectrum.

Findings

Established an analog of Carmona's formula.

Derived criteria for absolutely continuous spectrum.

Applied results to random Hilbert Schmidt perturbations.

Abstract

In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona's formula and deduce criteria for absolutely continuous spectrum which we apply to random Hilbert Schmidt perturbations of periodic scattering zippers.