On the dipole moment of quantized vortices generated by flows

Abstract

The polarization charge $\rho $ 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 ${{\rho }_{pol}}$ is proportional to $A{{\nabla }^{2}}n$, 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.