Diffusion of Quantum Vortices

Abstract

We determine the evolution of a cluster of quantum vortices initially placed at the centre of a larger vortex-free region. We find that the cluster spreads out spatially. This spreading motion consists of two effects: the rapid evaporation of vortex dipoles from the cluster and the slow expansion of the cluster itself. The latter is akin to a diffusion process controlled by the quantum of circulation. Numerical simulations of the Gross-Pitaevskii equation show that this phenomenon is qualitatively unaffected by the presence of sound waves, vortex annihilations, and boundaries, and it should be possible to create it in the laboratory.