2005 Fiscal Year Final Research Report Summary

Universalities in random matrix theory and quantum chaos

Research Project

Project/Area Number	14340114
Research Category	Grant-in-Aid for Scientific Research (B)
Allocation Type	Single-year Grants
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, 総合文化研究科, 教授 (30093298)
Co-Investigator(Kenkyū-buntansha)	INO Kazusumi The University of Tokyo, Graduate School of Arts and Sciences, Research associate, 総合文化研究科, 助手 (30334303)
Project Period (FY)	2002 – 2005
Keywords	mathematical physics / mesoscopic system / statistical mechanics / probability
Research Abstract	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.

(4 results)