1995/01/09 by P. W. Brouwer · 1 citation
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1103/physrevb.51.16878
published as Phys.Rev.B 51 (1995) 16878 · 15 pages, REVTeX-3.0, 2 figures, submitted to Physical Review B.
arxiv created 1995/01/09 · arxiv updated 2016/08/30
We consider the problem of the statistics of the scattering matrix S of a chaotic cavity (quantum dot), which is coupled to the outside world by non-ideal leads containing N scattering channels. The Hamiltonian H of the quantum dot is assumed to be an M x N hermitian matrix with probability distribution P(H) ~ det[lambda2 + (H - epsilon)2]^[-(beta M + 2- beta)/2], where lambda and epsilon are arbitrary coefficients and beta = 1,2,4 depending on the presence or absence of time-reversal and spin-rotation symmetry. We show that this ``Lorentzian ensemble'' agrees with microscopic theory for an ensemble of disordered metal particles in the limit M -> infinity, and that for any M >= N it implies P(S) ~ |det(1 - S† S)|^[-(beta M + 2 - beta)], where S is the ensemble average of S. This ``Poisson kernel'' generalizes Dyson's circular ensemble to the case S ≠ 0 and was previously obtained from a maximum entropy approach. The present work gives a microscopic justification for the case that the chaotic motion in the quantum dot is due to impurity scattering.