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

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