{"title":"论小耦合机制下有界类型的斯图尔米安哈密顿频谱","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":"{\"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}","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}
On the spectrum of Sturmian Hamiltonians of bounded type in a small coupling regime
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.