Resonant level model coupled to a Sachdev-Ye-Kitaev bath

System-plus-bath models play an important role in addressing fundamental questions in condensed matter physics. One challenging aspect is modelling the bath, for which the commonly used approaches are free-particle models and the Lindbladian formalism for open quantum systems. Here, we explore Sachdev-Ye-Kitaev (SYK) model as a new kind of quantum bath with unique properties, including the absence of quasiparticles, maximal chaos, and non-integrability, which make it a valuable framework for studying system-plus-bath interactions. First, we study the non-equilibrium dynamics of a resonant level model coupled to an SYK bath. From the Kadanoff-Baym equations for a noninteracting impurity, we find an analytical solution for an impurity occupation as a function of time. We observe a temperature dependent oscillatory decay of the impurity occupation, which differs from the temperature independent exponential decay observed in a free-particle bath and suggests interesting underlying physics. We further extend this problem into the case of interacting Anderson impurity coupled to an SYK bath, which we solve using NRG.