Universality of Random-Matrix Results for non-Gaussian Ensembles

Details Universality of Random-Matrix Results for non-Gaussian Ensembles Universality of Random-Matrix Results for non-Gaussian Ensembles

1994-12-20

arxiv.org/abs/cond-mat/9412088v1

Physics

Condensed Matter

10 pages, RevTeX, no figures

Scientific paper

10.1103/PhysRevLett.74.4118

We study random-matrix ensembles with a non-Gaussian probability distribution $P(H) \sim \exp (-N {\rm tr }\, V(H))$ 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 $N \rightarrow \infty$ 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.\ B {\bf 402}, 613 (1993)].

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