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.
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Shevchenko, S.I., Konstantinov, A.M. On the Dipole Moment of Quantized Vortices in the Presence of Flows. J Low Temp Phys 185, 384–391 (2016). https://doi.org/10.1007/s10909-016-1529-5
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DOI: https://doi.org/10.1007/s10909-016-1529-5