Grand canonical random matrices for intermediate level statistics

Abstract

The grand canonical treatment of the energy level statistics for the unitary ensemble of Hermitians of the form H= H 0+ tV (Yukawa's level-dynamics) reported by Forrester is extended to the orthogonal and the symplectic ensembles by using Dyson's quaternion representation. As a result, the two-level correlation functions are analyzed as functions of a single parameter a (=( β y / γ) 1/2: Yukawa's parameter of intermediacy), leading to the compressibility of the level gas for the three ensembles near the Poisson and the Wigner–Dyson limits.