In interacting quantum many-body systems, relaxation toward equilibrium reflects a competition between internal chaotic dynamics and environmental dissipation. While conventional Markovian baths typically produce exponential decay, non-Markovian dissipation can give rise to more intricate behavior, including algebraic relaxation. We study an open Sachdev-Ye-Kitaev (SYK) model coupled to a pseudogapped fermionic bath, using the Keldysh formalism to compute steady-state correlations in the large-$N$ limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate prerelaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.

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• Dissipative dynamics
• Open quantum systems
• Green's function methods
• Path-integral methods