Quench dynamics of superconducting fluctuations and optical conductivity in a disordered system*

There has been significant interest in the generation of very short-lived superconducting
states in solid-state films. Here we consider the role of non-equilibrium superconducting
fluctuations in such systems, generated by an interaction quench, considering the limit of large
static disorder. In particular, we argue that because of critical slowing down, the regime of the
fluctuation dominated \emph{normal state} is more important than might be na\"{i}vely thought. We
show how such a state might appear in the optical conductivity, and give the appropriate
non-equilibrium generalization of the Azlamazov-Larkin and Maki-Thompson fluctuation corrections to
the optical conductivity.