Coulomb blockade conductance peak distributions in quantum dots and the crossover between orthogonal and unitary symmetry

Closed expressions are derived for the distributions of resonance widths and Coulomb blockade conductance peak heights in quantum dots for the crossover regime between conserved and broken time-reversal symmetry. The results hold for leads with any number of possibly correlated and inequivalent channels and are obtained through a random matrix ensemble that interpolates between the Gaussian orthogonal and unitary ensembles. For any given value of the transition parameter the distributions are completely determined by the eigenvalues of the channel correlation matrix in each lead. Our analytic predictions are in good agreement with simulations of both random matrices and a chaotic billiard with a magnetic flux line.