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

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

1998-09-01

arxiv.org/abs/cond-mat/9809022v1

Waves in Random Media 9, 91 (1999)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

17 pages, RevTeX; 3 figures included; To appear in Waves in Random Media (special issue on disordered electron systems)

Scientific paper

10.1088/0959-7174/9/2/303

We calculate the joint probability distribution of the Wigner-Smith time-delay matrix $Q=-i\hbar S^{-1} \partial S/\partial \epsilon$ 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.

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