Statistics of complex levels of random matrices for decaying systems

We present analytical and numerical results for the level density of a certain class of random non-Hermitian matrices =H+i. The conservative partH belongs to the Gaussian orthogonal ensemble while the damping piece is quadratic in Gaussian random numbers and may describe the decay of resonances through various channels. In the limit of a large matrix dimension the level density assumes a surprisingly simple dependence on the relative strength of the damping and the number of channels. Moreover, we identify situations with cubic repulsion between the complex eigenvalues of , to within a logarithmic correction.