DYNAMICAL VORTICES IN SUPERFLUID FILMS

The coupling of superfluid film to a moving vortex is a gauge coupling entirely dictated by topology. From the definition of a linking number, one can define a gauge field ${\mathrm{A}}^{\mathrm{\ensuremath{\mu}}}$ , whose (2+1)-dimensional curl is the vortex three-current ${\mathrm{J}}^{\mathrm{\ensuremath{\mu}}}$ , and to which the superfluid is minimally coupled. We compute the superfluid density and current response to a moving vortex. Exploiting the analogy to (2+1)-dimensional electrodynamics, we compute the effective vortex mass M(\ensuremath{\omega}) and find that it is logarithmically divergent in the \ensuremath{\omega}\ensuremath{\rightarrow}0 limit, with a constant imaginary part, yielding a super-Ohmic dissipation in the presence of an oscillating superflow. Numerical integration of the nonlinear Schr\"odinger equation supports these conclusions. The interaction of vortices with impurities coupling to the density also is discussed.