1998/09/01 by Piet W. Brouwer, P. W. Brouwer, Klaus M. Frahm +2 · 6 citations
Chemistry · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Molecular spectroscopy and chirality #Quantum chaos and dynamical systems #chao-dyn #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.1088/0959-7174/9/2/303
published as Waves in Random Media 9, 91 (1999) · 17 pages, RevTeX; 3 figures included; To appear in Waves in Random Media (special issue on disordered electron systems)
arxiv created 1998/09/01 · openalex publication_date 1999/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We calculate the joint probability distribution of the Wigner-Smith time-delay matrix Q=−iℏS −1∂S/∂ε 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(ε)] of energy-dependent scattering matrices S(ε). The distribution of the inverse of the eigenvalues τ1,…,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.