{"title":"一维无序系统中特征态的局部化","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":"{\"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}","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}
Localization of Eigenstates in One-Dimensional Disordered Systems
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.
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