Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Brouwer, P.W.
AU - Frahm, K.M.
AU - Beenakker, C.W.J.
TI - Distribution of the quantum mechanical time-delay matrix for a chaotic cavity
JO - Waves in Random Media
PY - 1999-02-01T00:00:00///
VL - 9
IS - 2
SP - 91
EP - 104
N2 - We calculate the joint probability distribution of the Wigner-Smith time-delay matrix *Q* = -i*S*^{-1}*S*/ 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.
UR - https://www.ingentaconnect.com/content/tandf/wrm/1999/00000009/00000002/art00303
ER -