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A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations

Guhr, Thomas LU and Stockmann, HJ (2004) In Journal of Physics A: Mathematical and General1975-01-01+01:002007-01-01+01:00 37(6). p.2175-2190
Abstract
In a previous contribution (Stockmann H J 2002 J. Phys. A: Math. Gen. 35 5165), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the billiard shape. This result is now extended to the k-point correlation function. Using supersymmetric methods, we show that the correlations in the bulk are always identical to those of the Gaussian unitary ensemble (GUE) of random matrices. In passing from the band centre to the tail states, the density of states is depleted considerably and the two-point correlation function shows a gradual change from the GUE behaviour to that found for completely uncorrelated eigenvalues. This can be viewed as... (More)
In a previous contribution (Stockmann H J 2002 J. Phys. A: Math. Gen. 35 5165), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the billiard shape. This result is now extended to the k-point correlation function. Using supersymmetric methods, we show that the correlations in the bulk are always identical to those of the Gaussian unitary ensemble (GUE) of random matrices. In passing from the band centre to the tail states, the density of states is depleted considerably and the two-point correlation function shows a gradual change from the GUE behaviour to that found for completely uncorrelated eigenvalues. This can be viewed as similar to a mobility edge. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Physics A: Mathematical and General1975-01-01+01:002007-01-01+01:00
volume
37
issue
6
pages
2175 - 2190
publisher
IOP Publishing
external identifiers
  • wos:000189181900018
  • scopus:1342304910
ISSN
0305-4470
DOI
10.1088/0305-4470/37/6/015
language
English
LU publication?
yes
id
dac4ab52-506f-44ef-b923-fe9e79691942 (old id 286362)
date added to LUP
2007-08-02 13:59:00
date last changed
2017-12-05 10:51:07
@article{dac4ab52-506f-44ef-b923-fe9e79691942,
  abstract     = {In a previous contribution (Stockmann H J 2002 J. Phys. A: Math. Gen. 35 5165), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the billiard shape. This result is now extended to the k-point correlation function. Using supersymmetric methods, we show that the correlations in the bulk are always identical to those of the Gaussian unitary ensemble (GUE) of random matrices. In passing from the band centre to the tail states, the density of states is depleted considerably and the two-point correlation function shows a gradual change from the GUE behaviour to that found for completely uncorrelated eigenvalues. This can be viewed as similar to a mobility edge.},
  author       = {Guhr, Thomas and Stockmann, HJ},
  issn         = {0305-4470},
  language     = {eng},
  number       = {6},
  pages        = {2175--2190},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics A: Mathematical and General1975-01-01+01:002007-01-01+01:00},
  title        = {A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations},
  url          = {http://dx.doi.org/10.1088/0305-4470/37/6/015},
  volume       = {37},
  year         = {2004},
}