Crossover from Conserving to Lossy Transport in Circular Random Matrix Ensembles

TL;DR

This paper investigates how increasing loss in a quantum dot system transitions the transmission matrix from a constrained, conserving form to an unconstrained, lossy form, revealing a crossover in transport behavior.

Contribution

It introduces a model for the crossover from conserving to lossy transport in random matrix ensembles by varying the number of channels in a third lead.

Findings

Distribution of singular values approaches that of complex Gaussian matrices as channels increase.

The transition characterizes a shift from constrained to lossy transport regimes.

Provides insights into physical quantities related to transmission in quantum systems.

Abstract

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).