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 (sampl e-to-sample) fluctuations and weak-localization corrections on the con ductance, and also leads to time-dependent fluctuations (shot noise) o f the current. These effects are computed by means of a mapping onto a n unconstricted conductor with a renormalized mean free path. The mapp ing holds in both the metallic and the localized regimes, and permits a solution for an 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 distri bution of the conductance is known. The theory is supported by numeric al simulations.