Vortices in Nonlocal Condensate Models of Superfluid Helium

Helium Natalia G. Berloff and Paul H. Roberts Department of Mathematics University of California, Los Angeles, CA, 90095-1555 [email protected], [email protected], Abstract. Nonlocal nonlinear Schrödinger equations are considered as models of superfluid helium. The models contain a nonlocal interaction potential that leads to a phonon-roton-like dispersion relation. It is shown that for any such potential the generalized Gross-Pitaevskii (GP) model has non-physical features, specifically the development of catastrophic singularities and unphysical mass concentrations. The GP equation is remedied by introducing a higher order term in the local density approximation for the correlation energy. The resulting theory is applied in two ways. The family of superfluid vortex rings is derived. The nucleation of vortex rings by a moving ion is considered.