Arbitrary unitarily invariant random matrix ensembles and supersymmetry
(2006) In Journal of Physics A: Mathematical and General 39(42). p.1319113223 Abstract
 We generalize the supersymmetry method in random matrix theory to ensembles which are unitarily invariant, but otherwise arbitrary. Our exact approach extends a previous contribution in which we constructed a supersymmetric representation for the class of normdependent random matrix ensembles. Here, we derive a supersymmetric formulation under very general circumstances. A reduced probability density and a projector are identified that map the probability density from ordinary to superspace. Furthermore, it is demonstrated that setting up the theory in Fourier superspace has considerable advantages. General and exact expressions for the correlation functions are given. We also show how the use of hyperbolic symmetry can be circumvented in... (More)
 We generalize the supersymmetry method in random matrix theory to ensembles which are unitarily invariant, but otherwise arbitrary. Our exact approach extends a previous contribution in which we constructed a supersymmetric representation for the class of normdependent random matrix ensembles. Here, we derive a supersymmetric formulation under very general circumstances. A reduced probability density and a projector are identified that map the probability density from ordinary to superspace. Furthermore, it is demonstrated that setting up the theory in Fourier superspace has considerable advantages. General and exact expressions for the correlation functions are given. We also show how the use of hyperbolic symmetry can be circumvented in the present context in which the nonlinear sigma model is not used. We construct exact supersymmetric integral representations of the correlation functions for arbitrary positions of the imaginary increments in the Green's functions. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/378760
 author
 Guhr, Thomas ^{LU}
 organization
 publishing date
 2006
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Journal of Physics A: Mathematical and General
 volume
 39
 issue
 42
 pages
 13191  13223
 publisher
 IOP Publishing
 external identifiers

 wos:000241555500005
 scopus:33947260091
 ISSN
 03054470
 DOI
 10.1088/03054470/39/42/002
 language
 English
 LU publication?
 yes
 additional info
 The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Mathematical Physics (Faculty of Technology) (011040002)
 id
 16f1921b118e45668eeb8cda71bf1cfc (old id 378760)
 date added to LUP
 20160401 16:16:15
 date last changed
 20220128 18:28:39
@article{16f1921b118e45668eeb8cda71bf1cfc, abstract = {{We generalize the supersymmetry method in random matrix theory to ensembles which are unitarily invariant, but otherwise arbitrary. Our exact approach extends a previous contribution in which we constructed a supersymmetric representation for the class of normdependent random matrix ensembles. Here, we derive a supersymmetric formulation under very general circumstances. A reduced probability density and a projector are identified that map the probability density from ordinary to superspace. Furthermore, it is demonstrated that setting up the theory in Fourier superspace has considerable advantages. General and exact expressions for the correlation functions are given. We also show how the use of hyperbolic symmetry can be circumvented in the present context in which the nonlinear sigma model is not used. We construct exact supersymmetric integral representations of the correlation functions for arbitrary positions of the imaginary increments in the Green's functions.}}, author = {{Guhr, Thomas}}, issn = {{03054470}}, language = {{eng}}, number = {{42}}, pages = {{1319113223}}, publisher = {{IOP Publishing}}, series = {{Journal of Physics A: Mathematical and General}}, title = {{Arbitrary unitarily invariant random matrix ensembles and supersymmetry}}, url = {{http://dx.doi.org/10.1088/03054470/39/42/002}}, doi = {{10.1088/03054470/39/42/002}}, volume = {{39}}, year = {{2006}}, }