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 χ 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. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 970–973 (25 June 1996) Petersburg Nuclear Physics Institute, 188350, Gatchina, St. Petersburg District, Russia Published in English in the original Russian journal. Edited by Steve Torstveit.