Dissipation in Two-Dimensional Superfluids

Dissipation of energy by a thin film of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ on an oscillating planar substrate arises both from motion of free vortices and from polarization of bound pairs. Starting from a Langevin equation for vortex diffusion, and taking into account production of free vortices from bound pairs, we estimate this dissipation in various regimes of frequency, amplitude of vibration, and temperature.