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

Abstract

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's function approach, is used to explore the transient behavior on multiple time scales as the system approaches steady state. The dot population dynamics on short to intermediate times is governed by the dot-lead hybridization parameter ($\ensuremath{\Gamma}$) and by the typical phonon frequency (${\ensuremath{\omega}}_{c}$) and depends on the location of the energy level of the dot relative to the bias window. At longer times, the dynamics shows a distinct behavior depending on whether the system is in the adiabatic or nonadiabatic regime, with a quantum dot occupation that may depend on the initial preparation of the phonon degrees of freedom. A ``phase'' diagram of this effect as a function of the polaron shift ($\ensuremath{\lambda}$) for various phonon frequencies is derived, suggesting the existence of bistability on experimentally observable time scales.