Dynamics of emergent Cooper pairing at finite temperatures

We study the time evolution of a system of fermions with pairing interactions at a finite temperature. The dynamics is triggered by an abrupt increase in the BCS coupling constant. We show that if initially the fermions are in a normal phase, the amplitude of the BCS order parameter averaged over the Boltzmann distribution of initial states exhibits damped oscillations with a relatively short decay time. The latter is determined by the temperature, the single-particle level spacing, and the ground-state value of the BCS gap for the new coupling. In contrast, the decay is essentially absent when the system was in a superfluid phase before the coupling increase.