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Electronic and fluctuation dynamics following a quench to the superconducting phase

We investigate the dynamics of superconducting fluctuations in the attractive three-dimensional Hubbard model after a quench from the disordered phase to the ordered regime. While the long time evolution is well understood in terms of dissipative time-dependent Ginzburg-Landau models with unstable potentials, early times are more demanding due to the inseparable dynamics of the pairing fluctuations and the electronic quasiparticles. Our simulation using the time-dependent fluctuation exchange approximation treat both degrees of freedom on the same footing and reveal a non-thermal electronic regime causing a non-monotonous growth of the fluctuations. This feature is not directly captured from the Ginzburg-Landau theory, but nevertheless remains observable beyond the thermalization time of the electrons. We further explore how the growth of the order parameter fluctuations leads to an opening of a pseudo-gap in the electronic spectrum, and identify Andreev reflections as the dominant mechanism behind the gap opening.