Stationary vortex flows and macroscopic Zeno effect in Bose-Einstein condensates with localized dissipation

We theoretically demonstrate a possibility to observe the macroscopic Zeno effect in an effectively two-dimensional (pancake-shaped) repulsive Bose--Einstein condensate subjected to a strong narrow dissipation. We show that the dissipation can generate stable stationary nonlinear flows which bear either zero or non-zero topological charge (vorticity). The superfluid flows towards the dissipative defect compensate the atomic losses. The macroscopic Zeno effect manifests itself in a nonmonotonous dependence of the inward current density on the strength of the dissipation.