{"title":"On the spectrum of Sturmian Hamiltonians of bounded type in a small coupling regime","authors":"Alexandro Luna","doi":"arxiv-2408.01637","DOIUrl":null,"url":null,"abstract":"We prove that the Hausdorff dimension of the spectrum of a discrete\nSchr\\\"odinger operator with Sturmian potential of bounded type tends to one as\ncoupling tends to zero. The proof is based on the trace map formalism.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-03","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-2408.01637","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
We prove that the Hausdorff dimension of the spectrum of a discrete
Schr\"odinger operator with Sturmian potential of bounded type tends to one as
coupling tends to zero. The proof is based on the trace map formalism.
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