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In an absorptive system the Wigner reaction $K-$matrix (directly related tothe impedance matrix in acoustic or electromagnetic wave scattering) isnon-selfadjoint, hence its eigenvalues are complex. The most interesting regimearises when the absorption, taken into account as an imaginary part of thespectral parameter, is of the order of the mean level spacing. I show how toderive the mean density of the complex eigenvalues for reflection problems indisordered or chaotic systems with broken time-reversal invariance. Thecomputations are done in the framework of nonlinear $\sigma-$ model approach,assuming fixed $M$ and $N\to \infty$. Some explicit formulas are provided forzero-dimensional quantum chaotic system as well as for a semi-infinite quasi-1Dsystem with fully operative Anderson localization.

On the density of complex eigenvalues of Wigner reaction matrix in a disordered or chaotic system with absorption