On the momentum of solitons and vortex rings in a superfluid
arXiv:1407.8081 · doi:10.1134/S1063776114120152
Abstract
This paper is devoted to the calculation of the momentum of localized excitations, such as solitons and vortex rings, moving in a superfluid. The direct calculation of the momentum by integration of the mass flux density results in a badly-converging integral. I suggest a method for the renormalization of the integral with the explicit separation of a term related to the vortex line. This term can be calculated explicitly and gives the main contribution for the rings whose size is large compared to the healing length. I compare my method with the Jones and Roberts prescription for the renormalization. I investigate the case of a uniform superfluid, and that of a superfluid in a cylindrical trap. I discuss the calculation of the jump in the phase of the order parameter and obtain a simple estimate for this jump for a large ring in the trap.
Paper accepted for publication in the special issue of JETP devoted to 75-th anniversary of A.F. Andreev, 10 pages