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The nonequilibrium dynamics of a quantum dot with electron-phononinteractions described by a generalized Holstein model is presented. Acombination of methodologies including the reduced density matrix formalism,the multilayer multiconfiguration time-dependent Hartree method, and atime-dependent nonequilibrium Green function approach, is used to explore thetransient behavior on multiple timescales as the system approachessteady-state. The dot population dynamics on short to intermediate times isgoverned by the dot-lead hybridization parameter ($\Gamma$) and by the typicalphonon frequency ($\omega_{c}$) and depends on the location of the energy levelof the dot relative to the bias window. At longer times, the dynamics show adistinct behavior depending on whether the system is in the adiabatic ornon-adiabatic regime, with a quantum dot occupation that may depend on theinitial preparation of the phonons degrees of freedom. A "phase" diagram ofthis localization effect as a function of the polaron shift ($\lambda$) forvarious phonon frequencies is derived, suggesting the existence of bistabilityon experimentally observable timescales.

Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state