Thermalization in different phases of charged SYK model

We study thermalization of charged SYK model in two different phases. We show that both the highly chaotic liquid phase and the dilute gas phase thermalize. Surprisingly the dilute gas state thermalizes instantaneously. We argue that this phenomenon arises because the system in this phase consists of only long-lived quasi-particles at very low density. The liquid state thermalizes exponentially fast. We also show that the additional introduction of random mass deformation (q=2 SYK term) slows down thermalization but the system thermalizes exponentially fast. This is observed despite the fact that the addition of large q=2 SYK interaction forces spectral statistics to obey Poisson statistics. An interesting new observation is that the effective temperature is non-monotonic during thermalization in the liquid state. It has a bump at relatively long time before settling down to the final value. With non-zero chemical potential, the effective temperature oscillates noticeably before settling down to the final value.