Evaporation dynamics of the Sachdev-Ye-Kitaev model

In this paper, we study the evaporation dynamics of the Sachdev-Ye-Kitaev (SYK) model, with an initial temperature $T_\chi$, by coupling it to a thermal bath with lower temperature $T_\psi<T_\chi$ modeled by a larger SYK model. The coupling between the small system and the bath is turned on at time $t=0$. Then the system begins to envolve and finally becomes thermalized. Using the Keldysh approach, we analyze the relaxation process of the system for different temperatures and couplings. For marginal or irrelevant coupling, after a short-time energy absorption, we find a smooth thermalization of the small system where the energy relaxes before the system become thermalized. The relaxation rate of effective temperature is found to be bounded by $T$, while the energy thermalization rate increases without saturation when increasing the coupling strength. On the contrary, for the relevant coupling case, both energy and effective temperature show oscillations. We find this oscillations frequency to be coincident with the excitation energy of a Majorana operator.