1994 Fiscal Year Final Research Report Summary
Random Matrix Theory and its Applications
| Project/Area Number |
04640381
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | The University of Tokyo |
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Principal Investigator |
WADATI Miki University of Tokyo Graduate School of Science, Professor, 大学院・理学系研究科, 教授 (60015831)
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| Co-Investigator(Kenkyū-buntansha) |
NAGAO Taro Osaka University, Faculty of Science Research Associate, 理学部, 助手 (10263196)
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| Project Period (FY) |
1992 – 1994
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| Keywords | Random matrix / Level statistics / Logarithmic interaction / Orthogonal polynomial / Universality / Jastrow wave function / Mesoscopic system / Calogero model |
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| Research Abstract |
1. A statistical mechanics of one-dimensional particle system with logarithmic interactions is studied. Temperature dependence of the free energy is shown to be universal.
2. For ensembles related to classical orthogonal polynomials, the universality of fluctuations of level distributions is proved.
3. For the circular ensemble, correlation functions are expressed in terms of orthogonal or skew-orthogonal polynomials.
4. Ergodicity of ensembles is proved for ensembles related to classical orthogonal polynomials.
5. One-dimensional discrete Schrodinger equation is considered as a model for level statistics. There exists no local fluctuation of level statistics.
6. Distribution functions in real space corresponding to Jastrow wavefunctions are expressed in terms of orthogonal or skew-orthogonal polynomials.
7. Non-universality of the spectrum at the edge is shown and the spectrum is described by a parameter, which indicates a weak universality at the edge.
8. Motion of hamiltonian matrix under a perturbation is discussed.
9. Random matrix ensembles related to classical orthogonal polynomials, in particular ones corresponding to exponential-type distributions, are shown to be suitable models for conductivity in mesoscopic systems.
10. Relations betweem classical Calogero model and matrix model are discussed.
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Research Products
(38 results)
