title: Group integrals in chaotic quantum systems
creator: Kohler, Heiner
subject: ddc-530
subject: 530 Physics
description: 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). 
date: 2000
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/1406/1/thesis.pdf
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/1406/2/vorspann.pdf
identifier: DOI:10.11588/heidok.00001406
identifier: urn:nbn:de:bsz:16-opus-14062
identifier:   Kohler, Heiner  (2000) Group integrals in chaotic quantum systems.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/1406/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng