Transport in an inhomogeneous interacting one-dimensional system

Transport through a clean one-dimensional wire of interacting electrons connected to semi-infinite leads is investigated using a bosonization approach. An incident electron is transmitted as a sequence of partial charges. The de conductance is found to be entirely determined by the properties of the leads. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions, the central wire acts as a For abrupt resonator. When one of the connected wires has a tendency towards superconducting order, partial Andreev reflection of an incident electron occurs.