Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1996-03-11
Phys. Rev. E54 (1996) 2438
Nonlinear Sciences
Chaotic Dynamics
text: revtex, 21pp., figures -- postscript tar compressed with uufiles. Figure 1 not included, use your imagination, or it may
Scientific paper
10.1103/PhysRevE.54.2438
We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are obtained both theoretically and numerically. A simple formula describing the velocity distribution (and hence the distribution of the Wigner time delay) is derived, which is capable to explain the algebraic tail of the time delay distribution observed recently in microwave experiments. A dependence of the eigenphases on other external parameters is also discussed. We show that in the semiclassical limit (large number of channels) the curvature distribution of $S$--matrix eigenphases is the same as that corresponding to the curvature distribution of the underlying Hamiltonian and is given by the generalized Cauchy distribution.
Seba Petr
Zakrzewski Jakub
Zyczkowski Karol
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