Crossover from Conserving to Lossy Transport in Circular Random Matrix Ensembles
Steven H. Simon, Aris L. Moustakas
Abstract
In a quantum dot with three leads the transmission matrix t12 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 t12 becomes closer to a matrix of complex Gaussian random numbers with no constraints. We consider the distribution of the singular values of t12, 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).
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