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We develop a general framework for studying the equilibrium andnon-equilibrium properties of arbitrary networks of Sachdev-Ye-Kitaev clusterscoupled to thermal baths. We proceed to apply this technique to the problem ofenergy transport, which is known to be diffusive due to the strange metalbehavior of these models. We use the external baths to impose a temperaturegradient in the system and study the emerging non-equilibrium steady stateusing the Schwinger-Keldysh formalism. We consider two different configurationsfor the baths, implementing either a boundary or bulk driving, and show thatthe latter leads to a significantly faster convergence to the steady state.This setup allows us to compute both the temperature and frequency dependenceof the diffusion constant. At low temperatures, our results agree perfectlywith the previously known values for diffusivity in the conformal limit. Wealso establish a relationship between energy transport and quantum chaos byshowing that the diffusion constant is upper bounded by the chaos propagationrate at all temperatures. Moreover, we find a simple analytical form for thenon-equilibrium Green's functions in the linear response regime and use it toderive exact closed-form expressions for the diffusion constant in variouslimits. We mostly focus on uniform one-dimensional chains, but we also discusshigher-dimensional generalizations.

Energy Transport in Sachdev-Ye-Kitaev Networks Coupled to Thermal Baths