Single-mode delay time statistics for scattering by a chaotic cavity

We investigate the low-frequency dynamics for transmission or reflection of a wave by a cavity with chaotic scattering. We compute the probability dis tribution of the phase derivative phi ' = d phi /d omega of the scattered w ave amplitude, known as the single-mode delay time. In the case of a cavity connected to two single-mode waveguides we find a marked distinction betwe en detection in transmission and in reflection: The distribution P(phi ') v anishes for negative phi ' in the first case but not in the second case.