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An Extension of Level-spacing Universality

E. Brezin·S. Hikami
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Abstract

Dyson's short-distance universality of the correlation functions implies the universality of P(s), the level-spacing distribution. We first briefly review how this property is understood for unitary invariant ensembles and consider next a Hamiltonian H = H_0+ V , in which H_0 is a given, non-random, N by N matrix, and V is an Hermitian random matrix with a Gaussian probability distribution. n-point correlation function may still be expressed as a determinant of an n by n matrix, whose elements are given by a kernel $K(λ,μ)$ as in the H_0=0 case. From this representation we can show that Dyson's short-distance universality still holds. We then conclude that P(s) is independent of H_0.

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E. Brezin, S. Hikami. 1997-02-25. An Extension of Level-spacing Universality. https://doi.org/10.1103/physreve.56.264

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