Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption

We quantify the presence of direct processes in the S-matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P_S(S) of the S-matrix, i.e. S=\sqrt{R}e^{i\theta}, is studied in cavities with time-reversal symmetry for different antenna coupling strengths T_a or direct processes. The experimental results are compared with random-matrix calculations and with numerical simulations based on the Heidelberg approach including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with random-matrix predictions for all cases.