2005 Fiscal Year Final Research Report Summary
Universalities in random matrix theory and quantum chaos
| Project/Area Number |
14340114
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物性一般(含基礎論)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
HIKAMI Shinobu The University of Tokyo, Graduate School of Arts and Sciences, Professor, 総合文化研究科, 教授 (30093298)
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| Co-Investigator(Kenkyū-buntansha) |
INO Kazusumi The University of Tokyo, Graduate School of Arts and Sciences, Research associate, 総合文化研究科, 助手 (30334303)
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| Project Period (FY) |
2002 – 2005
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| Keywords | mathematical physics / mesoscopic system / statistical mechanics / probability |
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| Research Abstract |
The Universalities in random matrix theory appears in the correlation functions, and there are several universal classes depending upon the symmetries. In this research project, we have studied the random matrix theory (RMT) with an external source. We study RMT by a parameter β, which corresponds to GOE, GUE and GSE for β21,2 and 4, respectively. We have extended the integral formula of Harish Chandra-Itzykson-Zuber to a general value of β. The relation to Jack polynomial has been also studied. From the correlation function at the edge point, we obtain the intersection numbers on Riemann surfaces and applications to quantum chaos and random laser have been extensively studied.
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