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The Sachdev-Ye-Kitaev (SYK$_{4}$) model has attracted attention for its fastscrambling properties and its thermalization rate that is set only by thetemperature. In this work we ask the question of whether the SYK$_{4}$ model isalso a good thermal bath, in the sense that it allows a system coupled to it tothermalize. We address this question by considering the dynamics of a system of$N$ random non-interacting Majorana fermions coupled to an SYK$_{4}$ bath with$M$ Majorana fermions that we solve with Keldysh techniques in the limit of$M\gg N\gg 1$. We compare this nonequilibrium setting with a conventional bathmade of free non-interacting degrees of freedom with a continous spectrum. Weshow that the SYK$_{4}$ bath is more efficient in thermalising the system atweak coupling, due to its enhanced density of states at low frequency, while atstrong system-bath couplings both type of environments give rise to a similartime scale for thermalisation.

Are fast scramblers good thermal baths?