Time Asymmetry Structure of Intermediate Random Matrix Distributions

Abstract

The method of quaternion matrices by Dyson is adopted here for the Yukawa distribution, and the statistical properties of energy levels for orthogonal, unitary and symplectic classes are studied. To obtain a smooth interpolation between the Wigner–Dyson and the Poisson statistics by a single parameter a (Yukawa's parameter of intermediacy), a parameter \tildeθ( a ) which represents the degree of time-asymmetry is introduced [\tildeθ(0)=1 for the Poisson region, and \tildeθ(∞)=0 for the Wigner–Dyson limit]. On this basis, the two-level correlation functions are expressed as a function of θ( a ). As a consequence, the level compressibility for three universality classes is obtained as a function of a .