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Quantum mechanical time-delay matrix in chaotic scattering

P. W. Brouwer·K. M. Frahm·C. W. J. Beenakker
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Abstract

We calculate the probability distribution of the matrix Q = -i \hbar S^{-1} dS/dE for a chaotic system with scattering matrix S at energy E. The eigenvalues τ_j 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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P. W. Brouwer, K. M. Frahm, C. W. J. Beenakker. 1997-05-20. Quantum mechanical time-delay matrix in chaotic scattering. https://doi.org/10.1103/physrevlett.78.4737

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