On the dipole moment of quantized vortices generated by flows

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 ${{\rho }_{pol}}$isproportionalto$A{{\nabla }^{2}}n$,andthepolarization$$\mathbf{P}$$isproportionalto$A\nabla n$,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.