Classical stability of supercurrent in one dimension: a numerical study
  We report results of a classical simulation of thermal phase slips, and the associated relaxation of supercurrent, in a ring-shaped one-dimensional superfluid. We find that the classical relaxation rate vanishes in the uniform limit. This leaves the quantum relaxation, with momentum transfer to phonons, the only mechanism of supercurrent decay in the uniform system. In the presence of a smooth periodic potential, classical decay becomes possible, and we identify a family of moving critical droplets that can mediate it. 
S. Khlebnikov