Depinning of a superfluid vortex inside a circular defect

In this work we study the process of depinning of a quantum of circulation trapped inside a disk by an applied two-dimensional superflow. We use the Gross-Pitaevskii model to describe the neutral superfluid. The collective coordinate dynamics is derived directly from the condensate equation of motion, the nonlinear Schrödinger equation, and it is used to obtain an expression for the critical velocity as a function of the defect radius. This expression is compared with a numerical result obtained from the time-independent nonlinear Schrödinger equation. Below the critical velocity, we obtain the dependence of the semiclassical nucleation rate with the flow velocity at infinity. Above the critical velocity, the classical vortex depinning is illustrated with a numerical simulation of the time-dependent nonlinear Schrödinger equation.