  We study thermal diffusion dynamics of a single vortex in two dimensional XY
model. By numerical simulations we find an abnormal diffusion such that the
mobility decreases with time $t$ as $1/\ln t$. In addition we construct a one
dimensional diffusion-like equation to model the dynamics and confirm that it
conserves quantitative property of the abnormal diffusion. By analyzing the
reduced model, we find that the radius of the collectively moving region with
the vortex core grows as $R(t) \propto t^{1/2}$. This suggests that the
mobility of the vortex is described by dynamical correlation length as $1/\ln
R(t)$.
