Electron transport through ballistic quantum channels

We study the 1D transport through open channels of a quantum wire by a Luttinger liquid model. We introduce contact regions lying in between the non-interacting leads and the interacting quantum wire as Luttinger liquids whose properties are governed by the electron parameters in the leads. We place two barriers at the contacts to model imperfect coupling between the leads and the quantum wire. We then show that this model explains several interesting features of recent experiments. We discuss the criteria required to observe resonant transmission through such a quantum wire. We briefly discuss the role of an external magnetic field on transport.