Starting from the equation of Gor'kov and Eliashberg in a form introduced by Eilenberger, we derive a set of linearized equations for the deviation from the equilibrium value of the quasiparticle distribution function as well as of the order parameter. These equations resemble the Boltzmann equation and the Ginzburg-Landau equation, respectively, and they form a set of coupled equations. Two different modes can be distinguished, depending on whether the order parameter changes in magnitude or in phase. The equations are solved for the case of a stationary quasiparticle injection into a superconductor and the change in the electrochemical potential of the quasiparticles is calculated. Furthermore, we treat the problem of a current flowing perpendicular to a superconducting-normal interface in which a normal current is converted into a supercurrent, and we calculate the extra resistance of the interface.
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Schmid, A., Schön, G. Linearized kinetic equations and relaxation processes of a superconductor near T c . J Low Temp Phys 20, 207–227 (1975). https://doi.org/10.1007/BF00115264
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DOI: https://doi.org/10.1007/BF00115264