Dissipation–enhanced scrambling in the SYK model coupled to a lossy cavity

Many-body quantum chaos and information scrambling are typically studied in isolated quantum systems, where out-of-time-ordered correlators (OTOCs) diagnose how local information delocalizes over time. However, realistic quantum simulators and cavity quantum electrodynamics (cQED) platforms inevitably couple to environments, leading to dissipation such as photon leakage. While previous studies generally suggest that environmental coupling suppresses quantum scrambling, systems where the dissipative degrees of freedom simultaneously mediate the interactions between matter particles exhibit a much richer interplay. This paper investigates this phenomenon using the Yukawa-Sachdev-Ye-Kitaev (YSYK) model coupled to a lossy cavity.

The authors study a Majorana YSYK model consisting of N Majorana fermions coupled to R = gamma N bosons through random p-body interactions. Bosonic dissipation is modeled via a Markovian Lindblad master equation incorporating bosonic leakage at a rate kappa, which removes bosonic excitations from the system over time. Using the Schwinger-Keldysh path-integral formalism, the authors formulate the large-N theory in terms of collective Green's functions and self-energies, yielding closed Schwinger-Dyson equations that account for both coherent interaction dynamics and open-system relaxation.

Initializing the system in the steady state of the Lindbladian evolution, the analysis reveals two dominant energy scales: an effective interaction strength and a dissipative rate linked to the Purcell effect. The late-time fermionic relaxation rate exhibits anomalous behavior at weak leakage and nonmonotonic dependence at stronger dissipation. More remarkably, the quantum Lyapunov exponent—extracted from OTOC growth—remains strictly positive across all dissipation rates. For the QED case p = 2, the exponent decreases monotonically, whereas for chaotic systems with p > 2, intermediate dissipation can actually enhance the Lyapunov exponent through bath-induced quantum fluctuations before it eventually gets suppressed.