{"title":"一维随机薛定谔算子的特征值波动","authors":"Takuto Mashiko, Yuma Marui, Naoki Maruyama, Fumihiko Nakano","doi":"10.1063/5.0125197","DOIUrl":null,"url":null,"abstract":"As an extension to the paper by Breuer et al., Ann. Henri Poincare 22, 3763 (2021), we study the linear statistics for the eigenvalues of the Schrödinger operator with random decaying potential with order O(x−α) (α > 0) at infinity. We first prove similar statements as in Breuer et al., Ann. Henri Poincare 22, 3763 (2021) for the trace of f(H), where f belongs to a class of analytic functions: there exists a critical exponent αc such that the fluctuation of the trace of f(H) converges in probability for α > αc, and satisfies a central limit theorem statement for α ≤ αc, where αc differs depending on f. Furthermore we study the asymptotic behavior of its expectation value.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"22 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Eigenvalue fluctuations of 1-dimensional random Schrödinger operators\",\"authors\":\"Takuto Mashiko, Yuma Marui, Naoki Maruyama, Fumihiko Nakano\",\"doi\":\"10.1063/5.0125197\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"As an extension to the paper by Breuer et al., Ann. Henri Poincare 22, 3763 (2021), we study the linear statistics for the eigenvalues of the Schrödinger operator with random decaying potential with order O(x−α) (α > 0) at infinity. We first prove similar statements as in Breuer et al., Ann. Henri Poincare 22, 3763 (2021) for the trace of f(H), where f belongs to a class of analytic functions: there exists a critical exponent αc such that the fluctuation of the trace of f(H) converges in probability for α > αc, and satisfies a central limit theorem statement for α ≤ αc, where αc differs depending on f. Furthermore we study the asymptotic behavior of its expectation value.\",\"PeriodicalId\":16174,\"journal\":{\"name\":\"Journal of Mathematical Physics\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0125197\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1063/5.0125197","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Eigenvalue fluctuations of 1-dimensional random Schrödinger operators
As an extension to the paper by Breuer et al., Ann. Henri Poincare 22, 3763 (2021), we study the linear statistics for the eigenvalues of the Schrödinger operator with random decaying potential with order O(x−α) (α > 0) at infinity. We first prove similar statements as in Breuer et al., Ann. Henri Poincare 22, 3763 (2021) for the trace of f(H), where f belongs to a class of analytic functions: there exists a critical exponent αc such that the fluctuation of the trace of f(H) converges in probability for α > αc, and satisfies a central limit theorem statement for α ≤ αc, where αc differs depending on f. Furthermore we study the asymptotic behavior of its expectation value.
期刊介绍:
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