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Performance of Reservoir Discretizations in Quantum Transport Simulations



Justin E. Elenewski, Gabriela Wojtowicz, Marek Rams, Michael P. Zwolak


Quantum transport simulations require a level of discretization, often achieved through an explicit representation of the electronic reservoirs. These representations should converge to the same continuum limit, though there is a trade-off between a given finite representation and computational accuracy at a fixed computational cost. This fact becomes particularly onerous for many-body simulations and the atomic-scale modeling of nanoscale sensors. While various discretizations have been proposed to increase accuracy at reduced expense, there is no systematic evaluation of these methods. Here, we introduce an approach to compare reservoir discretizations on an even footing, using metrics beyond the current. We apply this approach to extended reservoir simulations (driven Liouville–von Neumann, etc.), where relaxation maintains a bias or temperature drop across the reservoirs, and assess popular models for non-interacting and many-body conditions. While some discretizations improve the accuracy of calculated currents, this is more ambiguous for the on-site densities that determine many-body interactions or for the overall state of the system (particularly at the reservoir sizes typical of simulations). Moreover, we develop an approach to approximate the optimal relaxation strength for numerical simulations by exploiting the control over virtual anomalies appearing in Kramers' turnover. We employ this to assess the performance of discretizations within many-body models, where targeting the appropriate relaxation regime is critical.
The Journal of Chemical Physics


Elenewski, J. , Wojtowicz, G. , Rams, M. and Zwolak, M. (2021), Performance of Reservoir Discretizations in Quantum Transport Simulations, The Journal of Chemical Physics, [online], (Accessed December 6, 2021)
Created September 29, 2021, Updated October 25, 2021