GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NONIDEAL LEADS

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[λ2+(H-)2]-(βM+2-β)/2, where λ and are arbitrary coefficients and β=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→, and that for any MN it implies P(S)det(1-S̄°S)-(βM+2-β), where S̄ is the ensemble average of S. This ''Poisson kernel'' generalizes Dyson's circular ensemble to the case S̄0 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. © 1995 The American Physical Society.