Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks

Fuente: arXiv
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Main Authors: Yang, Xinyu, Li, Long, Zhou, Qi
Format: Preprint
Published: 2026
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_version_ 1866915758634696704
author Yang, Xinyu
Li, Long
Zhou, Qi
author_facet Yang, Xinyu
Li, Long
Zhou, Qi
contents This paper introduces and rigorously analyzes a new class of one-dimensional discrete-time quantum walks whose dynamics are governed by a parametrized family of extended CMV matrices. The model generalizes the unitary almost Mathieu operator (UAMO) and exhibits a richer spectral phase diagram, closely resembling the extended Harper's model. It provides the first example of a solvable quasi-periodic quantum walk that exhibits a stable region of purely singular continuous spectrum.
format Preprint
id arxiv_https___arxiv_org_abs_2601_20081
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks
Yang, Xinyu
Li, Long
Zhou, Qi
Quantum Physics
Spectral Theory
81Q99, 47B36, 81Q35
This paper introduces and rigorously analyzes a new class of one-dimensional discrete-time quantum walks whose dynamics are governed by a parametrized family of extended CMV matrices. The model generalizes the unitary almost Mathieu operator (UAMO) and exhibits a richer spectral phase diagram, closely resembling the extended Harper's model. It provides the first example of a solvable quasi-periodic quantum walk that exhibits a stable region of purely singular continuous spectrum.
title Spectral Transitions and Singular Continuous Spectrum in A New Family of Quasi-periodic Quantum Walks
topic Quantum Physics
Spectral Theory
81Q99, 47B36, 81Q35
url https://arxiv.org/abs/2601.20081