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 transport. One powerful approach combines matrix product states with extended reservoirs. In this method, continuous reservoirs are represented by explicit, discretized counterparts where a chemical potential or temperature drop is maintained by relaxation. Currents are strongly influenced by relaxation when it is very weak or strong, resulting in a simulation-analog of Kramers' turnover in 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. The Kramers' turnover analog thus has five standard transport regimes, further constraining the parameters that lead to the intrinsic conductance. In particular, a relaxation strength proportional to the reservoir level spacing-the commonly assumed strategy-can prevent convergence to the continuum limit. This underscores that the turnover profiles enable identification of simulation parameters that achieve proper physical behavior.