1994/12/20 by Gregor Hackenbroich, G. Hackenbroich, H. A. Weidenmüller +1 · 6 citations
Chemistry · Physics and Astronomy · #Molecular spectroscopy and chirality #Quantum chaos and dynamical systems #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physrevlett.74.4118
10 pages, RevTeX, no figures
arxiv created 1994/12/20 · openalex publication_date 1995/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study random-matrix ensembles with a non-Gaussian probability distribution P(H)\ensuremath∼exp[\ensuremath-NtrV(H)], where N is the dimension of the matrix H and V(H) is independent of N. Using Efetov's supersymmetry formalism, we show that in the limit N\ensuremath→\ensuremath∞ both energy level correlation functions and correlation functions of S-matrix elements are independent of P(H) and hence universal on the scale of the local mean level spacing. This statement applies to each of the three generic ensembles (unitary, orthogonal, and symplectic). Universality is also found for correlation functions depending on some external parameter. Our results generalize previous work by Brezin and Zee [Nucl. Phys. B402, 613 (1993)].