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Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions

The existence of more than one steady-state in a many-body quantum system driven out-of-equilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this Letter, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the relaxation to steady-state and on the emergence of bistability is discussed.