Conductance determined by transmission: Probes and quantised constriction resistance

The domain of validity and the origin of different formulae relating conductance to transmissive behaviour is discussed. The large variety of possible measurement probes is emphasised. The quantised conductance of constrictions, studied in recent experiments, is treated. Theoretical discussions of that have stressed the supposedly unique role of G = (2e 2/h)Tr(tt) in this connection, regardless of the exact geometry or probe locations. This is shown to be incorrect, and a simple expression for the dependence of the 'quantised' conductance on the width of the wide region is given. We particularly emphasise the distinction between, on the one hand, experiments and discussions that are strictly limited to events at reservoirs and, on the other, those that have a concern with variations within the sample.