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 distribution of the phase derivative phi'=d phi/d omega of the scattered wave 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 between detection in transmission and in reflection: The distribution P(phi') vanishes for negative phi' in the first case but not in the second case. 
K.J.H. van Bemmel, H. Schomerus, C.W.J. Beenakker