Nonlinear dynamic properties of superconductors

A dynamic theory of superconductivity is formulated, based directly on the self-consistent field approximation in the real time representation. A kinetic equation is introduced, and the electron-phonon collision integral is obtained. Characteristic evolution times of the uniformly perturbed order parameter are determined. Depending on the initial quasiparticle distribution, the evolution of Δ can occur during times of the order of the inverse gap Δ-1, of the inverse energy spread γ-1 of the distribution function (if γ ≪ Δ), or during the inelastic (electron-phonon) collision time τe. These collisions become important for energy spreads γ∼△/τe.

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