2004/01/28 by Thomas Guhr, Hans-Jürgen Stöckmann, Hans-Juergen Stoeckmann
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #cond-mat.dis-nn
paper · pdf · doi:10.1088/0305-4470/37/6/015
published as J.Phys.A37:2175,2004 · 18 pages, 2 figures
openalex publication_date 2004/01/28 · arxiv created 2004/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. In a previous contribution (H.J. Stöckmann, J. Phys. A35, 5165 (2002)), 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.