{"title":"On the spectrum of electric quantum walk and related CMV matrices","authors":"Fan Yang","doi":"arxiv-2408.12724","DOIUrl":null,"url":null,"abstract":"In this note, we show that for a family of quantum walk models with electric\nfields, the spectrum is the unit circle for any irrational field. The result\nalso holds for the associated CMV matrices defined by skew-shifts.\nGeneralizations to CMV matrices with skew-shifts on higher dimensional torus\nare also obtained.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.12724","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, 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.
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