Quantum mechanical time-delay matrix in chaotic scattering
Abstract
We calculate the probability distribution of the matrix Q = -i S-1 dS/dE for a chaotic system with scattering matrix S at energy E. The eigenvalues τj of Q are the so-called proper delay times, introduced by E. P. Wigner and F. T. Smith to describe the time-dependence of a scattering process. The distribution of the inverse delay times turns out to be given by the Laguerre ensemble from random-matrix theory.
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