  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.
