Piet Brouwer

Title

The Classical Limit of Quantum Transport

Abstract

The interference of multiply scattered quantum mechanical matter waves causes small but noticeable corrections to the conductance of a metal at low temperatures. Historically, one separates the interference correction to the electrical conductance into `weak localization', a small negative correction to the conductance averaged over an ensemble of conductors with different impurity configurations, and the “conductance fluctuations”, the sample-to-sample fluctuations measured with respect to the ensemble average. What is the fate of quantum interference corrections in the limit that the wavelength of the electrons becomes small in comparison to all other relevant length scales? This limit is a “classical limit” similar to the transition from wave optics to ray optics that occurs when the typical size of optical elements becomes much larger than the wavelength of light. I'll show that, whereas the interference correction to the ensemble-averaged conductance (weak localization) disappears in this classical limit, the quantum interference contribution to the sample-specific conductance fluctuations remains surprisingly unaffected.