@article {Brouwer:1999:0959-7174:91,
title = "Distribution of the quantum mechanical time-delay matrix for a chaotic cavity",
journal = "Waves in Random Media",
parent_itemid = "infobike://tandf/wrm",
publishercode ="tandf",
year = "1999",
volume = "9",
number = "2",
publication date ="1999-02-01T00:00:00",
pages = "91-104",
itemtype = "ARTICLE",
issn = "0959-7174",
url = "https://www.ingentaconnect.com/content/tandf/wrm/1999/00000009/00000002/art00303",
author = "Brouwer, P.W. and Frahm, K.M. and Beenakker, C.W.J.",
abstract = "We calculate the joint probability distribution of the Wigner-Smith time-delay matrix Q = -iS-1S/ and the scattering matrix S for scattering from a chaotic cavity with ideal point contacts. To this end we prove a conjecture by Wigner about the unitary invariance property of the distribution functional P[S()] of energy-dependent scattering matrices S(). The distribution of the inverse of the eigenvalues 1, ... ,N of Q is found to be the Laguerre ensemble from random-matrix theory. The eigenvalue density () is computed using the method of orthogonal polynomials. This general theory has applications to the thermopower, magnetoconductance, and capacitance of a quantum dot.",
}