Covariant formulation of the dynamical equations of quantum vortices in type II superconductors

We have derived the closed system of covariant equations which describe the motion of quantum vortices regarded as a two-2dimensional polarized liquid. We have obtained the covariant expressions of the forces acting on the vortices; from the equilibrium condition of these forces we have deduced the equation satisfied by the velocity field of the fluid. It is shown that this velocity field depends on the friction coefficient, the density of vortices and the superconducting current. From this closed system of equations we derived the relaxation equation when a variable magnetic field is applied. Published in Astrofizika, Vol. 50, No. 3, pp. 381–391 (August 2007).