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

D. M. Sedrakian; R. A. Krikorian

doi:10.1103/PhysRevB.76.184501

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

D. M. Sedrakian, R. A. Krikorian

DOI 10.1103/PhysRevB.76.184501 · Physical Review B

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Abstract

We have derived the closed system of covariant equations which describe the motion of quantum vortices regarded as a two-dimensional polarized liquid. We have written 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, respectively, on the friction coefficient, the density of vortices, and the superconducting current. From this closed system of equations, we have derived the relaxation equation and solved it when a variable magnetic field is applied.