Hydrodynamic theory of motion of quantized vortex rings in trapped superfluid gases

摘要

I study vortex ring oscillations in a superfluid, trapped in an elongatedtrap, under the conditions of the Local Density Approximation. On the basis ofthe Hamiltonian formalism I develop a hydrodynamic theory, which is valid foran arbitrary superfluid and depends only on the equation of state. The problemis reduced to an ordinary differential equation for the ring radius. The casesof the dilute BEC and the Fermi gas at unitarity are investigated in detail.Simple analytical equations for the periods of small oscillations are obtainedand the equations of non-linear dynamics are solved in quadratures. The resultsagree with available numerical calculations. Experimental possibilities tocheck the predictions are discussed.