Statistical properties of chaotic scattering with one open channel

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Abstract
The correspondence between statistical properties of decaying states and fluctuations in resonance scattering is studied in a statistical model with one open channel. The model is described by an ensemble of random non-Hermitian matrices. The dependence of the correlation length on the coupling parameter both for the S matrix and the cross section is studied numerically. We show that maximal correlations in the scattering arise for a certain value of the coupling to the continuum, reflecting a specific change in the internal motion of intermediate decaying systems. Also, the Fourier transform of the two-point correlation function of the S matrix is analyzed both analytically and numerically. The self-averaging nature of this function is explicitly demonstrated.