Images and nonlocal vortex pinning in thin superfluid films

TL;DR

This paper derives a nonlocal equation of motion for vortices in thin superfluid films on disordered substrates, revealing how the condensate's compressibility leads to long-range pinning effects modeled via image potentials.

Contribution

It introduces a mean field framework to describe vortex dynamics with a nonlocal pinning potential caused by the condensate's compressibility and substrate disorder.

Findings

The effective pinning potential is nonlocal with a long-range tail.

The nonlocality is interpreted through image potentials.

The pinning energy relates to the Hamiltonian expectation value.

Abstract

For thin films of superfluid adsorbed on a disordered substrate, we derive the equation of motion for a vortex in the presence of a random potential within a mean field (Hartree) description of the condensate. The compressible nature of the condensate leads to an effective pinning potential experienced by the vortex which is nonlocal, with a long range tail that smoothes out the random potential coupling the condensate to the substrate. We interpret this nonlocality in terms of images, and relate the effective potential governing the dynamics to the pinning energy arising from the expectation value of the Hamiltonian with respect to the vortex wavefunction.