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

TL;DR

This paper investigates a non-equilibrium extension of the SYK model with quadratic perturbations, analyzing energy dissipation and resonance phenomena, revealing a peak near the polaron energy splitting and a dry friction-like effect under energy pumping.

Contribution

It introduces a non-equilibrium SYK$_4$+SYK$_2$ model, calculates energy dissipation rates, and uncovers novel resonance and friction-like effects under periodic modulation.

Findings

Energy dissipation rate peaks near polaron energy splitting

Resonance effects significantly influence energy dissipation

Dry friction-like behavior observed under energy pumping

Abstract

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 $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.