Non-analytic Vortex Core and a Nonlinear Vortex Flow in Bosonic Superfluids

We analyze the disorder limited motion of quantum vortices in a two-dimensional bosonic superfluid with a large healing length. It is shown that the excitations of low-energy degrees of freedom associated with the non-analytic reconstruction of the vortex core [Ann. Phys. {\bf 346}, 195 (2014)] determine strong non-linear effects in the vortex transport at velocities much smaller than Landau's critical velocity. Experiments are suggested to verify our predictions.