Anomalous relaxation in dissipative quantum chaos

We study the nonequilibrium dynamics of the Sachdev-Ye-Kitaev (SYK) model, N strongly coupled fermions with q-body random all-to-all interactions, coupled to a Markovian environment through jump operators either linear or quadratic in the Majoranas. We develop a dynamical mean-field theory for the Lindbladian time evolution on the Keldysh contour and numerically solve the saddle-point equations for $q=4$. For strong dissipation, the system relaxes exponentially to its steady state at a rate linear in the coupling, characteristic of a dissipation-driven relaxation. However, for weak coupling, there are oscillatory corrections to the exponential relaxation and we observe an anomalously large decay rate with a finite value even in the absence of an explicit coupling to the environment. Remarkably, close to the steady state, the real-time Lindbladian dynamics of this system is identical to the low-temperature dynamics in Euclidean time of a two-site non-Hermitian SYK with intersite coupling. Its gravity dual is similar to a Euclidean wormhole in a near-AdS2 background but with a wrong-sign Schwarzian. It is this configuration, dubbed a Keldysh wormhole, together with quantum chaos, that causes anomalous relaxation.