Quenches and (pre)thermalization in a mixed Sachdev-Ye-Kitaev model

We study the nonequilibrium quench dynamics of a mixed Sachdev-Ye-Kitaev model, with competing two-body random interactions leading to maximally chaotic non-Fermi liquid dynamics and a single body term which dominates at low temperatures and leads to Fermi liquid behavior. For different quench protocols, including sudden switching of two-body interaction and double quench protocols, we solve the large N real-time Dyson equation on the Keldysh contour and compute the dynamics of Green's functions from which we obtain effective temperature and relaxation rates. We show that the model thermalizes to a finite temperature equilibrium and that depending on the value of the quench parameters, the effective temperature can be below or above the Fermi-liquid to non-Fermi liquid crossover scale, which can then be accessed through the nonequilibrium dynamics. We identify quench protocols for which the heating dynamics slow down significantly- A n effect that we interpret as a signature of prethermalization.