Conductance Fluctuations, Weak Localization, and Shot Noise for a Ballistic Constriction in a Disordered Wire

This is a study of phase-coherent conduction through a ballistic point contact with disordered leads. The disorder imposes mesoscopic (sample-to-sample) fluctuations and weak-localization corrections on the conductance, and also leads to time-dependent fluctuations (shot noise) of the current. These effects are computed by means of a mapping onto an unconstricted conductor with a renormalized mean free path. The mapping holds both in the metallic and in the localized regime, and permits a solution for arbitrary ratio of mean free path to sample length. In the case of a single-channel quantum point contact, the mapping is onto a one-dimensional disordered chain, for which the complete distribution of the conductance is known. The theory is supported by numerical simulations. ***Submitted to Physical Review B.****