An ensemble of non-Hermitian Gaussian-random 2 x 2 matrices admitting the Wigner surmise

It is shown that an ensemble of complex pseudo-Hermitian (2 x 2) matrices with three independent elements drawn from a Gaussian random population can admit the level-spacing distribution P(x) = pix/2 e(-pix2/4) (Wigner surmise) despite the breaking of time-reversal-invariance. Notably, the Wigner surmise is known to be exact for an ensemble of Gaussian-random 2 x 2 real-symmetric matrices. Thus, the connection between the symmetry possessed by a Hamiltonian and the degree of level repulsion becomes non-unique. (C) 2003 Published by Elsevier Science B.V.