DYNAMICS OF 2-DIMENSIONAL VORTEX PAIRS IN A SPATIALLY VARYING POTENTIAL

We consider the dynamics of vortices in a superfluid He-4 film flowing over a substrate at zero temperature. The vortex trajectories are assumed to be governed by the Magnus-force equation with the effect of the substrate incorporated via the gradient of a potential. We use an equivalent Hamiltonian formulation to show that two vortices in a slowly varying potential can exhibit stochastic behavior. In this regard, there are differences between the cases of two vortices of the same sign and those of the opposite sign, the latter becoming stochastic more readily.