On out-of-equilibrium phenomena in pseudogap phase of complex SYK+U model

In this Letter we consider the out-of-equilibrium phenomena in the complex Sachdev-Ye-Kitaev (SYK) model supplemented with the attractive Hubbard interaction (SYK+U). This model provides the clear-cut transition from non-Fermi liquid phase in pure SYK to the superconducting phase through the pseudogap phase with non-synchronized Cooper pairs. We investigate the quench of the phase soft mode in this model and the relaxation to the equilibrium state. Using the relation with Hamiltonian mean field (HMF) model we show that the SYK+U model enjoys the several interesting phenomena, like violent relaxation, quasi-stationary long living states, out-of-equilibrium finite time phase transitions, non-extensivity and tower of condensates. We comment on the holographic dual gravity counterparts of these phenomena.