Landauer-type transport theory for interacting quantum wires:   Application to carbon nanotube Y junctions
  We propose a Landauer-like theory for nonlinear transport in networks of one-dimensional interacting quantum wires (Luttinger liquids). A concrete example of current experimental focus is given by carbon nanotube Y junctions. Our theory has three basic ingredients that allow to explicitly solve this transport problem: (i) radiative boundary conditions to describe the coupling to external leads, (ii) the Kirchhoff node rule describing charge conservation, and (iii) density matching conditions at every node. 
S. Chen, B. Trauzettel, and R. Egger