We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${ \cal H}=\hat{ H}-i\hat{ \Gamma}$, where both $\hat{ H}$ and $\hat{ \Gamma}$ are real symmetric, $\hat{ H}$ is random Gaussian and $\hat{ \Gamma}$ is such that $NTr \hat{ \Gamma}^2_2\sim Tr \hat{ H}_1^2$ when $N\to \infty$. When $\hat{ \Gamma}\ge 0$ 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 generalizes the well-known $\chi^2$ distribution to the case of overlapping resonances. We also consider a different class of "almost real" matrices when $\hat{ \Gamma}$ is random and uncorrelated with $\hat{ H}$.
Categories: chao-dyn cond-mat nlin.CD
