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A time-dependent inelastic electron transport theory for strongelectron-phonon interaction is established via the equations of motion methodcombined with the small polaron transformation. In this work, the dissipationvia electron-phonon coupling is taken into account in the strong couplingregime, which validates the small polaron transformation. The correspondingequations of motion are developed, which are used to study the quantuminterference effect and phonon-induced decoherence dynamics in molecularjunctions. Numerical studies show clearly quantum interference effect of thetransport electrons through two quasi-degenerate states with different couplingto the leads. We also found that the quantum interference can be suppressed bythe electron-phonon interaction where the phase coherence is destroyed byphonon scattering. This indicates the importance of electron-phonon interactionin systems with prominent quantum interference effect.

Dissipative time-dependent quantum transport theory: quantum interference and phonon induced decoherence dynamics