A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations
(2004) In Journal of Physics A: Mathematical and General 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/286362
- author
- Guhr, Thomas LU and Stockmann, HJ
- organization
- publishing date
- 2004
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Physics A: Mathematical and General
- 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
- 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
- dac4ab52-506f-44ef-b923-fe9e79691942 (old id 286362)
- date added to LUP
- 2016-04-01 16:12:17
- date last changed
- 2022-03-14 22:52:14
@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 General}},
title = {{A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations}},
url = {{http://dx.doi.org/10.1088/0305-4470/37/6/015}},
doi = {{10.1088/0305-4470/37/6/015}},
volume = {{37}},
year = {{2004}},
}