Statistical Distributions of Level Widths and Conductance Peaks in Irregularly Shaped Quantum Dots

Analytical expressions for width and conductance peak distributions for quantum dots with multichannel leads in the Coulomb blockade regime are presented for both limits of conserved and broken time-reversal symmetry. The results are valid for any number of nonequivalent and correlated channels, and the distributions are expressed in terms of the channel correlation matrix $M$ in each lead. The matrix $M$ is also given in closed form. A chaotic billiard is used as a model to test numerically the theoretical predictions.