Interplay between weak localization and quantized conductance

The interplay between weak localization and conductance quantization through a narrow channel is considered. The ''electrodes'' are essentially two half planes with slight disorder. In this system weak localization results from a coherent echo in the electrodes towards the channel. Therefore one has an interesting mixture of dimensions, the channel being quasi-one dimensional and the electrodes being two dimensional. As a consequence the quantum interference correction to the conductance is non-universal.