{"title":"黎曼模空间是量子遍历的","authors":"Dean Baskin, Jesse Gell-Redman, X. Han","doi":"10.4310/jdg/1683307003","DOIUrl":null,"url":null,"abstract":"In this note we show that the Riemann moduli spaces $M_{g, n}$ equipped with the Weil--Petersson metric are quantum ergodic for $3g+n \\geq 4$. We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Riemann moduli spaces are quantum ergodic\",\"authors\":\"Dean Baskin, Jesse Gell-Redman, X. Han\",\"doi\":\"10.4310/jdg/1683307003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we show that the Riemann moduli spaces $M_{g, n}$ equipped with the Weil--Petersson metric are quantum ergodic for $3g+n \\\\geq 4$. We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.\",\"PeriodicalId\":15642,\"journal\":{\"name\":\"Journal of Differential Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2019-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/jdg/1683307003\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/jdg/1683307003","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this note we show that the Riemann moduli spaces $M_{g, n}$ equipped with the Weil--Petersson metric are quantum ergodic for $3g+n \geq 4$. We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.
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