Time-resolved spectral density of interacting fermions following a quench to a superconducting critical point

Results are presented for the time evolution of fermions initially in a non-zero temperature normal phase, following the switch on of an attractive interaction. The dynamics are studied in the disordered phase close to the critical point, where the superfluid fluctuations are large. The analysis is conducted within a two-particle irreducible, large $N$ approximation. The system is considered from the perspective of critical quenches where it is shown that the fluctuations follow universal model A dynamics. A signature of this universality is found in a singular correction to the fermion lifetime, given by a scaling form $t^{(3-d)\mathrm{/}2}{S}_d({\epsilon }^{2}t)$, where $d$ is the spatial dimension, $t$ is the time since the quench, and $\epsilon$ is the fermion energy. The singular behavior of the spectral density is interpreted as arising due to incoherent Andreev reflections off superfluid fluctuations.