Quantum transport through quantum dot with electron-phonon interaction

We have studied the quantum transport through a quantum dot with electron- phonon interaction. For a generic model which is widely used to explain phonon coupled electron transport in quantum dots and single molecule junctions. We have shown that the system exhibit pronounced bistability even in out of equilibrium situations when the value of the bias is far from the linear response regime. The analysis revealed that the bistability increased for decreasing phonon frequency and depended on the electron-phonon coupling. We have developed an approach based on reduced density matrix formalism. The formalism is combined with the multilayer multi configuration time dependent Hartree method to numerically converge the memory Kernel at short times until it decays and infer from it the dynamics of the system at longer times and the approach to steady state. The relaxation to steady state and the appearance of the bistability depended on the phonon frequency and the strength of the electron-phonon coupling. We have found that the phenomenon persisted over time scale. The obtained results were found in good agreement with previously obtained results.