When can time-dependent currents be reproduced by the Landauer steady-state approximation?

We establish well-defined limits in which the time-dependent electronic currents across a molecular junction subject to a fluctuating environment can be quantitatively captured via the Landauer steady-state approximation. For this, we calculate the exact time-dependent non-equilibrium Green's function (TD-NEGF) current along a model two-site molecular junction, in which the site energies are subject to correlated noise, and contrast it with that obtained from the Landauer approach. The ability of the steady-state approximation to capture the TD-NEGF behavior at each instant of time is quantified via the same-time correlation function of the currents obtained from the two methods, while their global agreement is quantified by examining differences in the average currents. The Landauer steady-state approach is found to be a useful approximation when (i) the fluctuations do not disrupt the degree of delocalization of the molecular eigenstates responsible for transport and (ii) the characteristic time for charge exchange between the molecule and leads is fast with respect to the molecular correlation time. For resonant transport, when these conditions are satisfied, the Landauer approach is found to accurately describe the current, both on average and at each instant of time. For non-resonant transport, we find that while the steady-state approach fails to capture the time-dependent transport at each instant of time, it still provides a good approximation to the average currents. These criteria can be employed to adopt effective modeling strategies for transport through molecular junctions in interaction with a fluctuating environment, as is necessary to describe experiments.