Distribution of the quantum mechanical time-delay matrix for a chaotic cavity

Дата и время публикации : 1998-09-01T20:09:08Z

Авторы публикации и институты :
P. W. Brouwer
K. M. Frahm
C. W. J. Beenakker

Ссылка на журнал-издание: Waves in Random Media 9, 91 (1999)
Коментарии к cтатье: 17 pages, RevTeX; 3 figures included; To appear in Waves in Random Media (special issue on disordered electron systems)
Первичная категория: cond-mat.mes-hall

Все категории : cond-mat.mes-hall, chao-dyn, nlin.CD

Краткий обзор статьи: We calculate the joint probability distribution of the Wigner-Smith time-delay matrix $Q=-ihbar S^{-1} partial S/partial epsilon$ and the scattering matrix $S$ for scattering from a chaotic cavity with ideal point contacts. Hereto we prove a conjecture by Wigner about the unitary invariance property of the distribution functional $P[S(epsilon)]$ of energy dependent scattering matrices $S(epsilon)$. The distribution of the inverse of the eigenvalues $tau_1,…,tau_N$ of $Q$ is found to be the Laguerre ensemble from random-matrix theory. The eigenvalue density $rho(tau)$ is computed using the method of orthogonal polynomials. This general theory has applications to the thermopower, magnetoconductance, and capacitance of a quantum dot.

Category: Physics