We consider a non-equilibrium generalization of the mixed SYK4+SYK2 model and calculate the energy dissipation rate W(ω) that results due to periodic modulation of random quadratic matrix elements with a frequency ω. We find that W(ω) possesses a peak at ω close to the polaron energy spliting E1 found recently in [1], demonstrating physical significance of the energy E1. Next, we study the effect of energy pumping with a finite amplitude A1 at the resonance frequency ω = E1 and calculate, in presence of pumping, non-equilibrium boson distribution function and dissipation rate due to low-frequency parametric modulation. At sufficiently strong pumping, low-frequency dissipation rate recovers its large value, pertinent to the pure SYK4 limit.
[1] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.196602