Universalities in random matrix theory and quantum chaos

随机矩阵理论和量子混沌的普遍性

• 批准号: 14340114
• 负责人: HIKAMI Shinobu
• 金额: $ 8.7万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340114/
• 关键词: mathematical physics; mesoscopic system; statistical mechanics; probability; ランダム行列; 量子カオス; 行列模型

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.

随机矩阵理论中的普适性体现在相关函数中，根据对称性的不同有几个普适类。在本研究计划中，我们研究了具有外部源的随机矩阵理论（RMT）。我们用一个参数β来研究RMT，它分别对应于β 21，2和4时的GOE，GUE和GSE.本文将Harish Chandra-Itzykson-Zuber的积分公式推广到β的一般值。研究了它与Jack多项式的关系。从边缘点的关联函数出发，我们得到了黎曼曲面上的相交数，并在量子混沌和随机激光中得到了广泛的应用。

项目成果

New correlation functions for random matrices and integrals over super groups

随机矩阵和超群积分的新相关函数

• 发表时间: 2003
• 期刊: J.Phys.A : Math.Gen. 36
• 作者: E.Brezin;S.HiKami
• 通讯作者: S.HiKami

E.Brezin, S.Hikami: "An Extension of the Harish Chandra-Itzykson-Zuber Integral"Communications in Mathematical Physics. (in press). (2003)

E.Brezin、S.Hikami：“Harish Chandra-Itzykson-Zuber 积分的扩展”数学物理通信。

An extension of the Harish Chandra-Itqyson-Zuber integral

Harish Chandra-Itqyson-Zuber 积分的扩展

• 发表时间: 2003
• 期刊: Commun.Math.Phys. 235
• 作者: E.Brezin;S.Hikami
• 通讯作者: S.Hikami

E.Brezin, S.Hikami: "New correlation functions for random matrices and integrals over super groups"Journal of physics : Mathematical and General. 36巻・3号. 711-752 (2003)

E.Brezin、S.Hikami：“随机矩阵和超群积分的新相关函数”《物理学杂志：数学与综合》第 36 卷，第 3 期。711-752 (2003)

An Extension of the HarishChandra-Itzykson-Zuber Integral

HarishChandra-Itzykson-Zuber 积分的扩展

• 发表时间: 2002
• 作者: É. Brézin;S. Hikami
• 通讯作者: S. Hikami