Group integrals in chaotic quantum systems

We derive a recursion formula for a class of group integrals both in ordinary space and in superspace. These group integrals represent the generalization of Bessel functions to matrix and supermatrix spaces. Thereby we derive exact expressions for the one and two--point eigenvalue correlator of a random matrix model. The model consists of a sum of two random matrices. One of them is diagonal and models the regular part. The other one is a Gaussian random matrix (GOE or GSE) modelling the chaotic admixture. We prove that in ordinary space the recursion formula is an integral solution of a Hamiltonian system related to Calogero--Sutherland models for arbitrary coupling beta>0. We calculate closed expressions for some group integrals over the unitary symplectic group. Moreover we generalize the Gelfand--Tzetlin coordinate system and construct a parametrization of the unitary orthosymplectic group UOSp(k_1/2k_2).

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2000

Author dc:creator

• Kohler, Heiner

Contributors dc:contributor

• Guhr, Thomas

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/1406

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:1406