Statistics of S-matrix poles in few-channel chaotic scattering: Crossover from isolated to overlapping resonances

We derive an explicit expression for the distribution of resonance widths in a chaotic quantum system coupled to continua via M equivalent open channels. It describes a crossover from the chi(2) distribution (regime of isolated resonances) to a broad, power-law-like distribution typical for the regime of overlapping resonances. The first moment is found to reproduce exactly the Moldauer-Simonius relation between the mean resonance width and the transmission coefficient. (C) 1996 American Institute of Physics.