Currents and correlations in Luttinger liquids and carbon nanotubes at finite temperature and size: a bosonization study

We consider problems of one dimensional interacting fermions confined to a finite size, multichannel geometry. Concentrating on Luttinger liquids and carbon nanotubes, we use nontrivial boundary conditions to represent the effect of external leads, and apply our framework to transport problems in a Josephson junction setup. We present an exact computation of all correlation functions, including finite-size and temperature effects, for two sets of solvable boundary conditions. In all cases, we compute physical quantities like the Josephson current and the pairing order parameter profile.