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 -> infinity 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 -> infinity Hamiltonian for t >= 0 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 -> infinity Hamiltonian is a perfect thermalizer even for nonequilibrium states generated in this manner.