Direct measurement of vortex diffusivity in thin films ofHe4

We report direct measurements of vortex diffusivity, D, as a function of temperature through the Kosterlitz-Thouless transition. We find that D is a rapidly varying function of temperature near the transition. It is very small well below the transition, increases to ∼ħ/m at the static transition temperature, and apparently diverges at the point where the superfluid density vanishes. The diffusivity appears to be insensitive to the presence of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ impurities and to the nature of the substrate.