  The nonequilibrium dynamics of a quantum dot with electron-phonon
interactions described by a generalized Holstein model is presented. A
combination of methodologies including the reduced density matrix formalism,
the multilayer multiconfiguration time-dependent Hartree method, and a
time-dependent nonequilibrium Green function approach, is used to explore the
transient behavior on multiple timescales as the system approaches
steady-state. The dot population dynamics on short to intermediate times is
governed by the dot-lead hybridization parameter ($\Gamma$) and by the typical
phonon frequency ($\omega_{c}$) and depends on the location of the energy level
of the dot relative to the bias window. At longer times, the dynamics show a
distinct behavior depending on whether the system is in the adiabatic or
non-adiabatic regime, with a quantum dot occupation that may depend on the
initial preparation of the phonons degrees of freedom. A "phase" diagram of
this localization effect as a function of the polaron shift ($\lambda$) for
various phonon frequencies is derived, suggesting the existence of bistability
on experimentally observable timescales.
