  We have experimentally measured transport of superfluid, bosonic atoms in a
mesoscopic system: a small channel connecting two large reservoirs. Starting
far from equilibrium (superfluid in a single reservoir), we observe first
resistive flow transitioning at a critical current into superflow,
characterized by oscillations. We reproduce this full evolution with a simple
electronic circuit model. We compare our fitted conductance to two different
microscopic phenomenological models. We also show that the oscillations are
consistent with LC oscillations as estimated by the kinetic inductance and
effective capacitance in our system. Our experiment provides an attractive
platform to begin to probe the mesoscopic transport properties of a dilute,
superfluid, Bose gas.
