Distribution of the quantum mechanical time-delay matrix for a chaotic cavity
| dc.creator | Brouwer, P. W. | |
| dc.creator | Frahm, K. M. | |
| dc.creator | Beenakker, C. W. J. | |
| dc.date | 1998-09-01 | |
| dc.date.accessioned | 2026-07-07T03:11:26Z | |
| dc.date.available | 2026-07-07T03:11:26Z | |
| dc.description | We calculate the joint probability distribution of the Wigner-Smith time-delay matrix $Q=-i\hbar S^{-1} \partial S/\partial ε$ 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 $P[S(ε)]$ of energy dependent scattering matrices $S(ε)$. The distribution of the inverse of the eigenvalues $τ_1,...,τ_N$ of $Q$ is found to be the Laguerre ensemble from random-matrix theory. The eigenvalue density $ρ(τ)$ is computed using the method of orthogonal polynomials. This general theory has applications to the thermopower, magnetoconductance, and capacitance of a quantum dot. | |
| dc.description | 17 pages, RevTeX; 3 figures included; To appear in Waves in Random Media (special issue on disordered electron systems) | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9809022 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9809022 | |
| dc.identifier | Waves in Random Media 9, 91 (1999) | |
| dc.identifier | doi:10.1088/0959-7174/9/2/303 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28575 | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Distribution of the quantum mechanical time-delay matrix for a chaotic cavity | |
| dc.type | text |