Parametric hypersensitivity in many-body bath-mediated transport: The quantum Rabi model

We demonstrate that non-equilibrium steady states of the dissipative Rabi model show dramatic spikes in transport rates over narrow parameter ranges. Similar results are found for the Holstein and Dicke models. This is found to be due to avoided energy level crossings in the corresponding closed systems, and correlates with spikes in the entanglement entropy of key eigenstates, a signature of strong mixing and resonance among system degrees of freedom. Further, contrasting the Rabi model with the Jaynes-Cummings model reveals this behavior as being related to quantum integrability.