2012 Fiscal Year Final Research Report
Universality of Random Matrices and Semiclassical Quantum Theory
| Project/Area Number |
20540372
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Nagoya University |
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Principal Investigator |
NAGAO Taro 名古屋大学, 多元数理科学研究科, 教授 (10263196)
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| Co-Investigator(Renkei-kenkyūsha) |
TATE Tatsuya 名古屋大, 大学院・多元数理科学研究科, 准教授 (00317299)
SAITO Keiji 慶應義塾大学, 理工学部, 准教授 (90312983)
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| Project Period (FY) |
2008 – 2012
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| Keywords | ランダム行列 / 半古典量子論 |
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| Research Abstract |
The eigenvalue correlation functions for the matrix ensemble continuously interpolating between the asymmetric real and symmetric real random matrices were evaluated and the asymptotic behavior in the limit of large matrix dimension was derived. The method of semiclassical diagrammatic expansion was applied to classically chaotic quantum systems and the universal properties were reproduced. The random matrix methods were applied to the theory of complex networks and the eigenvalue densities of the matrices describing the networks were shown to be analytically evaluated in the limit of large average degree.
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