Inertial Josephson Relation for FIR Frequencies

Consideration of the balance of forces on superconducting condensate at low frequencies leads to the well-known Josephson Relation. Using the Ginzburg-Landau expression for the current, an expression relating the electric field to the vortex velocity via the magnetic field is obtained. This result is the Josephson Relation, supplemented by a term accounting for the inertia of charge carriers. This Inertial Josephson Relation may be used at all frequencies and may be viewed as the Josephson Relation extended to the case of sub-gap high-frequency response. When applied to vortex dynamics it yields the same conductivity as solution of the Ginzburg-Landau theory.