Resonant tunnelling between Luttinger liquids: solvable case

We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonisation and re-fermionisation methods, we find a mapping to a Kondo-type problem which possesses a non-trivial Toulouse-type solvable point. At this point, we obtain an analytic expression for the non-linear current-voltage characteristics and analyse the differential conductance and the width of the resonance peak as functions of bias and gate voltages, temperature, and barrier asymmetry. We also determine the exact scaling function for the linear conductance.