Thermalization of many many-body interacting Sachdev-Ye-Kitaev models

We investigate the nonequilibrium dynamics of complex Sachdev-Ye-Kitaev (SYK) models in the q limit, where q/2 denotes the order of the random Dirac fermion interaction. We extend previous results by Eberlein et al. Phys. Rev. B 96, 205123 (2017) to show that a single SYK q Hamiltonian for t0 is a perfect thermalizer in the sense that the local Green's function is instantaneously thermal. The only memories of the quantum state for t<0 are its charge density and its energy density at t=0. Our result is valid for all quantum states amenable to a 1/q expansion, which are generated from an equilibrium SYK state in the asymptotic past and acted upon by an arbitrary combination of time-dependent SYK Hamiltonians for t<0. Importantly, this implies that a single SYK q Hamiltonian is a perfect thermalizer even for nonequilibrium states generated in this manner.