We present a microscopic theory of 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. This originates from the tunneling process that condensate elements are coherently converted into phonon excitations and vice versa, yielding a linear current-bias relation. As a consequence, we predict zero thermopower and Lorenz number at zero temperature, a breakdown of the bosonic Wiedemann-Franz law. These effects are found to dominate the transport properties up to temperatures of the order of the chemical potential, with a leading power law temperature dependence behavior for heat transport coefficients. The consequences on heat and particle transport measurements in bosonic two-terminal setups should be readily observable in existing experiments.
|Publication status||Published - 2019 Jun 21|
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