Project/Area Number  08454106 
Research Category 
GrantinAid for Scientific Research (B)

Section  一般 
Research Field 
物性一般(含基礎論)

Research Institution  The University of Tokyo 
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)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Fiscal Year 
1996 – 1998

Project Status 
Completed(Fiscal Year 1998)

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)

Keywords  random matrix / matrix model / random system / level correlation / universality / super conductor vortex excitation / quantized Hall effect / quantum chaos / ランダム マトリックス / マトリックス模型 / ランダム系 / レベル相関 / ユニバーサリティ / 超伝導体磁束励起 / 量子ホール効果 / 量子カオス / 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 
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 npoint 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.
