Quantum Transport through Quantum Dot with Electron-Phonon Interaction (Bulletin of Pure and Applied Sciences – Physics, 2020)
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.