Sub-Ohmic to super-Ohmic crossover behavior in nonequilibrium quantum systems with electron-phonon interactions

The transition from weakly damped coherent motion to localization in the context of the spin-boson model has been the subject of numerous studies with distinct behavior depending on the form of the phonon-bath spectral density Jω∞ωs. Sub-Ohmic (s<1) and Ohmic (s=1) spectral densities show a clear localization transition at zero temperature and zero bias, while for super-Ohmic (s>1) spectral densities this transition disappears. In this paper, we consider the influence of the phonon-bath spectral density on the nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by the extended Holstein model. Using the reduced density matrix formalism combined with the multilayer multiconfiguration time-dependent Hartree approach, we investigate the dynamic response, the time scales for relaxation, as well as the existence of multiple long-lived solutions as the system-bath coupling changes from the sub- to the super-Ohmic cases. Bistability is shown to diminish for increasing powers of s similar to the spin-boson case. However, the physical mechanism and the dependence on the model parameters such as the typical bath frequency ωc and the polaron shift λ are rather distinct.