Tunneling through a barrier in Tomonaga-Luttinger liquid connected to   reservoirs
  The transport through a barrier is studied for a Tomonaga-Luttinger liquid of finite length connected to reservoirs. An effective action for the phase variable at the barrier is derived for spatially varying electric field. In the d.c. limit only the total voltage drop between the left and right reservoirs appears in the action. We discuss crossovers of the renormalization group flow and hence of the temperature and wire length dependence of the conductance, taking into account the location of the barrier. 
Akira Furusaki and Naoto Nagaosa