  We investigate the dynamics of a phonon-mediated superconductor driven out of
equilibrium. The electronic hopping amplitude is ramped down in time, resulting
in an increased electronic density of states. The dynamics of the coupled
electron-phonon model is investigated by solving Migdal-Eliashberg equations
for the double-time Keldysh Green's functions. The increase of the density of
states near the Fermi level leads to an enhancement of superconductivity when
the system thermalizes to the new state at the same temperature. We provide a
time- and momentum-resolved view on this thermalization process, and show that
it involves fast processes associated with single-particle scattering and much
slower dynamics associated with the superconducting order parameter. The
importance of electron-phonon coupling for the rapid enhancement and the
efficient thermalization of superconductivity is demonstrated, and the results
are compared to a BCS time-dependent mean-field approximation.
