Quantum mechanical time-delay matrix in chaotic scattering

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.

4 pages, RevTeX; to appear in Phys. Rev. Lett

References in corpus (1)

• Parametric Correlations of Phase Shifts and Statistics of Time Delays in Quantum Chaotic Scattering: Crossover between Unitary and Orthogonal Symmetries

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