  Results are presented for the quench dynamics of a clean and interacting
electron system, where the quench involves varying the strength of the
attractive interaction along arbitrary quench trajectories. The initial state
before the quench is assumed to be a normal electron gas, and the dynamics is
studied in a regime where long-range order is absent, but nonequilibrium
superconducting fluctuations need to be accounted for. A quantum kinetic
equation using a two-particle irreducible formalism is derived. Conservation of
energy, particle-number, and momentum emerge naturally, with the conserved
currents depending on both the electron Green's functions and the Green's
functions for the superconducting fluctuations. The quantum kinetic equation is
employed to derive a kinetic equation for the current, and the transient
optical conductivity relevant to pump-probe spectroscopy is studied. The
general structure of the kinetic equation for the current is also justified by
a phenomenological approach that assumes model-F in the Halperin-Hohenberg
classification, corresponding to a non-conserved order-parameter coupled to a
conserved density. Linear response conductivity and the diffusion coefficients
in thermal equilibrium are also derived, and connections with Aslamazov-Larkin
fluctuation corrections are highlighted. Results are also presented for the
time-evolution of the local density of states. It is shown that Andreev
scattering processes result in an enhanced density of states at low
frequencies. For a quench trajectory corresponding to a sudden quench to the
critical point, the density of states is shown to grow in a manner where the
time after the quench plays the role of the inverse detuning from the critical
point.
