On the Dipole Moment of Quantized Vortices in the Presence of Flows

Abstract

The polarization charge $\rho _\mathrm {pol}$ of an inhomogeneous superfluid system is expressed as a function of the order parameter $\Phi (\mathbf{r}_1 ,\mathbf{r}_2 )$. It is shown that if the order parameter changes on macroscopic distances, the polarization charge $\rho _\mathrm{pol}$ is proportional to $A\nabla ^2n$, and the polarization $\mathbf{P}$ is proportional to $A\nabla n$, where n is the density of the system. For noninteracting atoms, the proportionality coefficient A is independent of density, and in the presence of interaction A is proportional to n. The change of the Bose gas density is found in the presence of a flow $\mathbf{w}=\mathbf{v}_n -\mathbf{v}_s$ passing the vortex. It is found that a vortex in a superfluid film creates an electric potential above the film. This potential has the form of a potential of a dipole, allowing to assign a dipole moment to the vortex. The dipole moment is a sum of two terms, the first one is proportional to the relative flow velocity $\mathbf{w}$ and the second one is proportional to $\left[ {{\mathbf {\kappa }} \times \mathbf{w}} \right]$, where $\mathbf{\kappa }$ is the vortex circulation.