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Arbitrary unitarily invariant random matrix ensembles and supersymmetry

Guhr, Thomas LU (2006) In Journal of Physics A: Mathematical and General 39(42). p.13191-13223
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 norm-dependent 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 norm-dependent 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:
author
organization
publishing date
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
0305-4470
DOI
10.1088/0305-4470/39/42/002
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
16f1921b-118e-4566-8eeb-8cda71bf1cfc (old id 378760)
date added to LUP
2016-04-01 16:16:15
date last changed
2021-04-13 01:41:53
@article{16f1921b-118e-4566-8eeb-8cda71bf1cfc,
  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 norm-dependent 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         = {0305-4470},
  language     = {eng},
  number       = {42},
  pages        = {13191--13223},
  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/10.1088/0305-4470/39/42/002},
  doi          = {10.1088/0305-4470/39/42/002},
  volume       = {39},
  year         = {2006},
}