Bourget, Olivier; Howland, James S.; Joye, Alain Spectral analysis of unitary band matrices. (English) Zbl 1029.47016 Commun. Math. Phys. 234, No. 2, 191-227 (2003). Summary: This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems. These doubly infinite matrices essentially depend on an infinite sequence of phases which govern their spectral properties. We prove the spectrum to be purely singular for random phases and purely absolutely continuous in case they provide the doubly infinite matrix with a periodic structure in the diagonal direction. We also study some properties of the singular spectrum of such matrices considered as infinite in one direction only. Cited in 1 ReviewCited in 34 Documents MSC: 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47A10 Spectrum, resolvent 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 47N50 Applications of operator theory in the physical sciences Keywords:monodromy operators; absolutely continuous spectrum; singular spectrum PDFBibTeX XMLCite \textit{O. Bourget} et al., Commun. Math. Phys. 234, No. 2, 191--227 (2003; Zbl 1029.47016) Full Text: DOI arXiv