Dephasing in a Molecular Junction Viewed from a Time-Dependent and a Time-Independent Perspective

The current through a molecular junction can be determined numerically in a multitude of ways. Some of these methods like the Landauer scheme are only valid for coherent transport and the steady state regime while other schemes are able to treat time-dependent electronic currents across molecular junctions subject to fluctuating environments. In time-independent formalisms, the effect of thermal environments can be introduced in several ways. Here we focus on the vibronic dephasing model within a Green's function approach. This time-independent scheme is contrasted with the time-dependent nonequilibrium Green's function (TD-NEGF) approach in which the effect of the thermal environment manifests itself in fluctuating site energies. It is found that the time-averaged results of the TD-NEGF approach agree excellently with those from the vibronic model. This numerical comparison helps us to better understand the connection between these different pure dephasing schemes, which both have advantages and specific applications.