Statistics of Transmission Eigenvalues for a Disordered Quantum Point Contact

We study the distribution of transmission eigenvalues of a quantum point contact with nearby impurities. In the semi-classical case (the chemical potential lies at the conductance plateau) we find that the transmission properties of this system are obtained from the ensemble of Gaussian random reflection matrices. The distribution only depends on the number of open transport channels and the average reflection eigenvalue and crosses over from the Poissonian for one open channel to the form predicted by the circuit theory in the limit of large number of open channels.