German Title: Gruppenintegrale in Chaotischen Quantensystemen

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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 twopoint 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 CalogeroSutherland models for arbitrary coupling beta>0. We calculate closed expressions for some group integrals over the unitary symplectic group. Moreover we generalize the GelfandTzetlin coordinate system and construct a parametrization of the unitary orthosymplectic group UOSp(k_1/2k_2).
Translation of abstract (English)
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 twopoint 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 CalogeroSutherland models for arbitrary coupling beta>0. We calculate closed expressions for some group integrals over the unitary symplectic group. Moreover we generalize the GelfandTzetlin coordinate system and construct a parametrization of the unitary orthosymplectic group UOSp(k_1/2k_2).
Item Type:  Dissertation 

Supervisor:  Guhr, Priv. Doz Thomas 
Date of thesis defense:  6 December 2000 
Date Deposited:  11 Jan 2001 00:00 
Date:  2000 
Faculties / Institutes:  Service facilities > MaxPlanckInstitute allgemein > MPI for Nuclear Physics 
Subjects:  530 Physics 
Controlled Keywords:  Gruppentheorie, Quantenchaos, Supersymmetrie 
Uncontrolled Keywords:  Dysons Brownsche Bewegung, Gruppenintegrale, Zufallsmatrixtheoriegroup integrals, quantum chaos, random matrix theory, supersymmetry 