| Project/Area Number |
08454106
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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, 大学院・総合文化研究科, 教授 (30093298)
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| Co-Investigator(Kenkyū-buntansha) |
HIGUCHI Saburo The University of Tokyo, Graduate School of Arts and Sciences, Research Associat, 大学院・総合文化研究科, 助手 (70272474)
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| Project Period (FY) |
1996 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1997: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1996: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | random matrix / matrix model / random system / level correlation / universality / super conductor vortex excitation / quantized Hall effect / quantum chaos / ランダム行列 / フレドホルム行列式 / 非エルミートハミルトニアン / ランダム行列理論 |
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| Research Abstract |
For the random matrix model, various universality and their crossover have been studied in the relation to the phase transition of the random system. The random matrix with external source has been studied for the n-point covelation function, the form factor and the level spacing distribution, and the exact integral replesentation for them are obtained. In the large N limit, the universality of the covelation function has been discussed. The esternal source makes the basic approach for the crossover form the deterministic Hamiltonion to random Hamiltonian. As application, the complex random matrix and the superconductor vortex excitation have been unsidued. The crossover form the clear ease to the dirty case for the vortex excitation has been studied. Related to the cluiral in variouce, two states of the quanfized Hall effect(spin state) is also studied for the deusify of state and for the conductivity.
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