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.
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Document Type: Miscellaneous
Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, USA
Laboratoire de Physique Quantique, UMR 5626 du CNRS, Université Paul Sabatier, 31062 Toulouse Cedex 4, France
Instituut-Lorentz, Leiden University, PO Box 9506, 2300 RA Leiden, The Netherlands
February 1, 1999