Energy transport across two interacting quantum baths without quasiparticles

Energy transport in quantum many-body systems with well defined quasiparticles has recently attracted interest across different fields, including out of equilibrium conformal field theories, one-dimensional quantum lattice models, and holographic matter. Here we study energy transport between two interacting quantum baths without quasiparticles made by two Sachdev-Ye-Kitaev (SYK) models at temperatures TL≠TR and connected by a Fermi-liquid system. We obtain an exact expression for the nonequilibrium energy current, valid in the limit of large bath and system size and for any system-bath coupling V. We show that the peculiar criticality of the SYK baths has direct consequences on the thermal conductance, which above a temperature T∗(V)∼V4 is parametrically enhanced with respect to the linear-T behavior expected in systems with quasiparticles. Interestingly, below T∗(V) the linear thermal conductance behavior is restored, yet transport is not due to quasiparticles. Rather the system gets strongly renormalized by the bath and becomes non-Fermi liquid and maximally chaotic. Finally, we discuss the full nonequilibrium energy current and show that its form is compatible with the structure J=φ(TL)-φ(TR), with φ(T)∼Tγ and power law crossing over from γ=3/2 to γ=2 below T∗.