  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.
