Critical and near-critical relaxation of holographic superfluids

We investigate the relaxation of holographic superfluids after quenches, when the end state is either tuned to be exactly at the critical point, or very close to it. By solving the bulk equations of motion numerically, we demonstrate that in the former case the system exhibits a power law falloff, as well as an emergent discrete scale invariance. The latter case is in the regime dominated by critical slowing down, and we show that there is an intermediate time range before the onset of late-time exponential falloff, where the system behaves similarly to the critical point with its power law falloff. We further postulate a phenomenological Gross-Pitaevskii-like equation (corresponding to model F of Hohenberg and Halperin) that is able to make quantitative predictions for the behavior of the holographic superfluid after near-critical quenches into the superfluid and normal phase. Intriguingly, all parameters of our phenomenological equation, which describes the nonlinear time evolution, may be fixed with information from the static equilibrium solutions and linear response theory.