Energy transport in Sachdev-Ye-Kitaev networks coupled to thermal baths

We develop a general framework for studying the equilibrium and non-equilibrium properties of arbitrary networks Sachdev-Ye-Kitaev clusters coupled to thermal baths. proceed apply this technique problem energy transport, which is known be diffusive due strange metal behavior these models. use external baths impose temperature gradient in system study emerging steady state using Schwinger-Keldysh formalism. consider two different configurations baths, implementing either boundary or bulk driving, show that latter leads significantly faster convergence state. This setup allows us compute both frequency dependence diffusion constant. At low temperatures, our results agree perfectly with previously values diffusivity conformal limit. also establish relationship between transport quantum chaos by showing constant upper bounded propagation rate at all temperatures. Moreover, we find simple analytical form Green's functions linear response regime it derive exact closed-form expressions various limits. mostly focus on uniform one-dimensional chains, but discuss higher-dimensional generalizations.