Crossover from Conserving to Lossy Transport in Circular Random Matrix Ensembles

In a quantum dot with three leads the transmission matrix t_{12} between two of these leads is a truncation of a unitary scattering matrix S, which we treat as random. As the number of channels in the third lead is increased, the constraints from the symmetry of S become less stringent and t_{12} becomes closer to a matrix of complex Gaussian random numbers with no constraints. We consider the distribution of the singular values of t_{12}, which is related to a number of physical quantities. Changing the number of channels in the third lead corresponds to increasing the amount of loss in the system (and is distinct from prior uses of a third lead to model dephasing).