Transport in a bosonic superfluid point contact

We discuss heat and particle transport of a weakly interacting, low temperature Bose-Einstein condensate in a quantum point contact. We show that the presence of gapless phonon modes in the condensate yields a contact resistance at zero temperature and a corresponding nonzero DC conductance. As a consequence, we predict zero thermopower and Lorenz number at zero temperature, a breakdown of the bosonic Wiedemann-Franz law. The consequences on heat and particle transport measurements in bosonic two-terminal setups should be readily observable in existing experiments.