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Energy Transport between Strange Quantum Baths

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 \emph{strange quantum baths} without quasiparticles, made by two Sachdev-Ye-Kitaev (SYK) models at temperatures $T_L\neq T_R$ 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 $T^*(V)\sim V^4$ 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 strange 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 $\mathcal{J}=Φ(T_L)-Φ(T_R)$, with $Φ(T)\sim T^γ$ and power law crossing over from $γ=3/2$ to $γ=2$ below $T^*$.