We study the dynamics of a single and a corotating vortex pair in a dipolar Bose–Einstein condensate in the framework of a dissipative Gross–Pitaevskii equation. This simple model enables us to simulate the effect of finite temperature on the vortex dynamics. We study the effect of dipolar interactions on the dynamics of a single vortex in the presence of phenomenological dissipation. In the case of a corotating vortex pair, initial asymmetry in the locations of the vortices can lead to different decay rates for the constituent vortices, as is the case for the condensates interacting via pure contact interactions. We observe that the anisotropic interaction between the component vortices manifests itself as the perceptible difference in the trajectories traversed by the vortices in the condensate at finite temperatures.
We investigate the dissipative dynamics of a corotating vortex pair in a highly oblate axisymmetric Bose-Einstein condensate trapped in a harmonic potential. The initial vortex state is prepared by creating a doubly charged vortex at the center of the condensate and letting it dissociate into two singly charged vortices. The separation of the vortex pair gradually increases over time and its increasing rate becomes higher with increasing the sample temperature
T. The evolution of the vortex state is well described with a dissipative point vortex model including longitudinal friction on the vortex motion. For condensates of sodium atoms having a chemical potential of $\ensuremath{\mu}\ensuremath{\approx}{k}_{B}\ifmmode\times\else\texttimes\fi{}120$ nK, we find that the dimensionless friction coefficient $\ensuremath{\alpha}$ increases from 0.01 to 0.03 over the temperature range of
200nK<T<450 nK.