Vacuum tunneling of vortices in two-dimensional ⁴He superfluid films

At low temperature T we expect vacuum tunneling processes to occur in superfluid ⁴He films. We distinguish between extrinsic processes, in which single vortices nucleate by tunneling off boundaries in the system, and intrinsic processes, in which vortex/anti-vortex pairs nucleate far from boundaries. It is crucial to incorporate the varying effective mass of the vortex in tunneling calculations. The intrinsic processes are the superfluid analogue of the Schwinger mechanism in quantum field theory; here they appear as a quantum phase transition at T = 0, driven by an external supercurrent. We calculate the tunneling rate for these processes, and describe a means of testing the predictions using a specific "vortex counting" experiment.