Regensburg 2010 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 19: Quantum Chaos
DY 19.13: Talk
Wednesday, March 24, 2010, 17:30–17:45, H38
Moments of the Wigner delay times — Gregory Berkolaiko1 and •Jack Kuipers2 — 1Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA — 2Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be well described by random matrix theory. Here we present a semiclassical derivation showing the validity of random matrix results. In order to simplify the semiclassical treatment, we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies. In the semiclassical approximation, the elements of the scattering matrix are given in terms of the classical scattering trajectories, requiring one to study correlations between sets of such trajectories. We describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number. This allows us to derive a polynomial equation satisfied by the generating function of the moments. Along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory, we infer that the scattering matrix is unitary to all orders in the semiclassical approximation.
Arxiv:0910.0060