Quantum Quenches and Thermalization in SYK models

We study non-equilibrium dynamics in SYK models using quantum quench. We consider models with two, four, and higher fermion interactions ($q=2, 4$, and higher) and use two different types of quench protocol, which we call step and bump quenches. We analyse evolution of fermion two-point functions without long time averaging. We observe that in $q=2$ theory the two-point functions do not thermalize. We find thermalization in $q=4$ and higher theories without long time averaging. We calculate two different exponents of which one is equal to the coupling and the other is proportional to the final temperature. This result is more robust than thermalization obtained from long time averaging as proposed by the eigenstate thermalization hypothesis(ETH). Thermalization achieved without long time averaging is more akin to mixing than ergodicity.