{"title":"Localization of Eigenstates in One-Dimensional Disordered Systems","authors":"M. Goda","doi":"10.1143/PTPS.72.232","DOIUrl":null,"url":null,"abstract":"Exact results are obtained on the localization of eigenstates in one dimensional infinite disordered systems with diagonal and off-diagonal random nesses. A Furstenberg-type theorem is established for the product of matrices associated with a multi-Markov-chain. As a result, Matsuda and Ishii's theory is generalized to examine the systems with both randomnesses. Harmonic chains, tightly binding electronic systems and Heisenberg-Mattis model are considered as typical examples.","PeriodicalId":20614,"journal":{"name":"Progress of Theoretical Physics Supplement","volume":"72 1","pages":"232-246"},"PeriodicalIF":0.0000,"publicationDate":"2013-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1143/PTPS.72.232","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Progress of Theoretical Physics Supplement","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1143/PTPS.72.232","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
Exact results are obtained on the localization of eigenstates in one dimensional infinite disordered systems with diagonal and off-diagonal random nesses. A Furstenberg-type theorem is established for the product of matrices associated with a multi-Markov-chain. As a result, Matsuda and Ishii's theory is generalized to examine the systems with both randomnesses. Harmonic chains, tightly binding electronic systems and Heisenberg-Mattis model are considered as typical examples.