On absolutely continuous spectrum for one-channel unitary operators
arXiv:2405.08898 · doi:10.1007/s11005-024-01866-0
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.
36 pages, 5 figures