Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation

We consider a non-equilibrium generalization of the mixed $SYK_4 + SYK_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $E_1$ found recently in [1], demonstrating physical significance of the energy $E_1$. Next, we study the effect of energy pumping with a finite amplitude $A_1$ at the resonance frequency $\omega = E_1$ 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 $SYK_4$ limit.

References

1. A. V. Lunkin, A. Yu. Kitaev, M. V. Feigel'man, Phys. Rev. Lett., 125 (2020), 196602, arXiv: 2006.14535