Generalized circular ensemble of scattering matrices for a chaotic cavity with nonideal leads
Abstract
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 nonideal leads containing N scattering channels. The Hamiltonian H of the quantum dot is assumed to be an M×M Hermitian matrix with probability distribution P(H)~det[λ^{2}+(Hɛ)^{2}]^{(βM+2β)/2}, where λ and ɛ are arbitrary coefficients and β=1,2,4 depending on the presence or absence of timereversal and spinrotation symmetry. We show that this ``Lorentzian ensemble'' agrees with microscopic theory for an ensemble of disordered metal particles in the limit M>∞, and that for any M>=N it implies P(S)~det(1S¯ ^{°}S)^{(βM+2β)}, 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 chaotic motion in the quantum dot is due to impurity scattering.
 Publication:

Physical Review B
 Pub Date:
 June 1995
 DOI:
 10.1103/PhysRevB.51.16878
 arXiv:
 arXiv:condmat/9501025
 Bibcode:
 1995PhRvB..5116878B
 Keywords:

 05.45.+b;
 72.10.Bg;
 General formulation of transport theory;
 Condensed Matter
 EPrint:
 15 pages, REVTeX3.0, 2 figures, submitted to Physical Review B.