S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances

We study complex eigenvalues of large N x N symmetric random matrices of th e form H = H - i<(Gamma)over cap>, where both H and <(Gamma)over cap> are r eal symmetric. H is a random Gaussian and <(Gamma)over cap> is such that N Tr <(Gamma)over cap>(2) similar to Tr H-2 when N --> infinity. When <(Gamma )over cap> greater than or equal to 0 the model can be used to describe the universal statistics of S-matrix poles (resonances) in the complex energy plane. We derive the ensuing distribution of the resonance widths which gen eralizes the well known chi(2) distribution to the case of overlapping reso nances. We also consider a different class of 'almost real' matrices when < (Gamma)over cap> is random and uncorrelated with <(Gamma)over cap>.