T*model of the energy distributions of excitations in nonequilibrium superconductors

The coupled set of nonlinear kinetic Boltzmann equations governing the distributions of quasiparticles and phonons in a driven superconductors has been numerically solved. When the coupling between the superconductor and the thermal bath is weak, we find that the numerical solutions are well approximated by an extension of Parker's $T^{*}$ model. This model leads to simple analytic forms in which the quasiparticle distribution is given by a Fermi function at temperature $T^{*}$, and the phonon distribution is a weighted average of Bose distributions at temperatures $T^{*}$ and the ambient bath temperature $T_a$.