Ehrenfest theorem for inhomogeneous superconductors and supercurrent force on Andreev reflected quasiparticles

Quasiclassical equations of motion are derived for quasiparticle wave packets in inhomogeneous superconductors with electromagnetic fields. Besides the Lorentz forces on electrons and holes there are two off-diagonal pair potential forces. The first one is due to gradients of the modulus of the pair potential and responsible for electron-hole scattering from inhomogeneities of the pair potential. The second one results from interactions with the ground state condensate and is proportional to the gauge invariant Cooper pair velocity of surface supercurrents in the interfaces between normal and superconducting regions. The most favorable experimental conditions for the observation of this new force may be found inN-S junctions composed of clean normal metals and type II superconductors with high critical fields, large London penetration depths, and large energy gaps.