Annihilation Process of Quantum Vortices in Dissipative Gross-Pitaevskii Equation Model

Abstract

In two dimensional superfluid, annihilation processes of vortices are investigated by numerical simulation within the dissipative Gross-Pitaevskii equation (GPE) model. First, quantum vortex solution is obtained and its fitting function is found. Second, the simulation show that positive and negative vortices accelerate in both x,y directions, until they annihilate into a soliton and then a crescent-shaped shock wave. The processes are found to be controlled by the dissipative parameter and the general Magnus force. For the behavior of separation distance between vortices d(t), an universal scaling exponent 1/2 is found which is same with the three dimensional cases. Third, system's energy is surprisingly found to be determined by system's configuration and their relation are obtained. Then we derive the general Magnus force which decreases with the increases of d(t) for large d(t) and increases with the increases of d(t) for small d(t).