Dual current anomalies and quantum transport within extended reservoir simulations

Quantum transport simulations are rapidly evolving and now encompass well-controlled tensor network techniques for many-body limits. One powerful approach combines matrix product states with extended reservoirs. In this method, continuous reservoirs are represented by explicit, discretized counterparts and a chemical potential or temperature drop is maintained by external relaxation. Currents are strongly influenced by relaxation when it is very weak or strong, resulting in a simulation analog of Kramers' turnover for solution-phase chemical reactions. At intermediate relaxation, the intrinsic conductance -- that given by the Landauer or Meir-Wingreen expressions -- moderates the current. We demonstrate that strong impurity scattering (i.e., a small steady-state current) reveals anomalous transport regimes within this methodology at weak-to-moderate and moderate-to-strong relaxation. The former is due to virtual transitions and the latter to unphysical broadening of the populated density of states. Thus, the turnover analogue has five standard transport regimes, further constraining the parameters that lead to the intrinsic conductance. In particular, the common strategy of choosing a relaxation strength proportional to the reservoir level spacing can prevent convergence to the continuum limit. This underscores the utility of turnover profiles when identifying parameters that deliver physical behavior.