eprintid: 1406
rev_number: 13
eprint_status: archive
userid: 1
dir: disk0/00/00/14/06
datestamp: 2001-01-11 00:00:00
lastmod: 2014-04-03 10:36:17
status_changed: 2012-08-14 15:00:56
type: doctoralThesis
metadata_visibility: show
creators_name: Kohler, Heiner
title: Group integrals in chaotic quantum systems
title_de: Gruppenintegrale in Chaotischen Quantensystemen
ispublished: pub
subjects: ddc-530
divisions: i-851340
adv_faculty: af-13
keywords: Dysons Brownsche Bewegung, Gruppenintegrale, Zufallsmatrixtheoriegroup integrals, quantum chaos, random matrix theory, supersymmetry
cterms_swd: Gruppentheorie
cterms_swd: Quantenchaos
cterms_swd: Supersymmetrie
abstract: 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). 
abstract_translated_text: 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).
abstract_translated_lang: eng
class_scheme: pacs
class_labels: 02.20.-a, 05.45.Mt, 02.50.Sk, 02.30.Nw
date: 2000
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00001406
ppn_swb: 1643183230
own_urn: urn:nbn:de:bsz:16-opus-14062
date_accepted: 2000-12-06
advisor: HASH(0x55e0f7f1fbe0)
language: eng
bibsort: KOHLERHEINGROUPINTEG2000
full_text_status: public
citation:   Kohler, Heiner  (2000) Group integrals in chaotic quantum systems.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/1406/1/thesis.pdf
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/1406/2/vorspann.pdf