Effect of a Voltage Probe on the Phase-Coherent Conductance of a Ballistic Chaotic Cavity

The effect of an invasive voltage probe on the phase-coherent conduction through a ballistic chaotic cavity is investigated by random-matrix theory. The entire distribution P(G) of the conductance G is computed for the case that the cavity is coupled to source and drain by two point contacts with a quantized conductance of 2 e^2/h, both in the presence (beta = 1) and absence (beta = 2) of time-reversal symmetry. The loss of phase-coherence induced by the voltage probe causes a crossover from P(G) ~ G^(-1 + beta/2) to a Gaussian centered at G = e^2/h with a beta-dependent width. ***Submitted to Physical Review B.***Comment: 9 pages, REVTeX-3.0, 4 postscript figures appended as self-extracting archive, INLO-PUB-941020

GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NON-IDEAL 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 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[lambda^2 + (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 - \bar S^{\dagger} S)|^[-(beta M + 2 - beta)], where \bar S is the ensemble average of S. This ``Poisson kernel'' generalizes Dyson's circular ensemble to the case \bar S \neq 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.Comment: 15 pages, REVTeX-3.0, 2 figures, submitted to Physical Review B