Detailed solutions for non-equilibrium superconductivity. I. Temperature-dependent solutions

The kinetic equations for non-equilibrium superconductivity are solved numerically using two techniques. The first, based on a 'histogram' quadrature, is used to find the excess distribution functions at various temperatures for a BCS superconductor perturbed by NIS tunnelling, phonon injection and microwave irradiation and these solutions are then used to predict the change to first order in the applied field of the gap and the nuclear spin relaxation rate. The second method uses a variational approach and compares favourably with the first. The possibility of using non-equilibrium superconductivity as a probe of the deviations from a BCS density of states is briefly discussed.