The problem of quantum chaotic scattering with direct processes reduced to the one without

We show that the study of the statistical properties of the scattering matrix S for quantum chaotic scattering in the presence of direct processes (charaterized by a nonzero average S matrix <S>) can be reduced to the simpler case where direct processes are absent (<S> = 0). Our result is verified with a numerical simulation of the two-energy autocorrelation for two-dimensional S matrices. It is also used to extend Wigner's time delay distribution for one-dimensional S matrices, recently found for <S> = 0, to the case <S> not equal to zero; this extension is verified numerically. As a consequence of our result, future calculations can be restricted to the simpler case of no direct processes.