Elenewski Justin E, Wójtowicz Gabriela, Rams Marek M, Zwolak Michael
Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA.
Jagiellonian University, Institute of Theoretical Physics, Łojasiewicza 11, 30-348 Kraków, Poland.
J Chem Phys. 2021 Sep 28;155(12):124117. doi: 10.1063/5.0065799.
Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that typical reservoir discretizations have little impact on numerical costs for certain computational tools. The choice of a relaxation parameter is nonetheless crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.
量子输运模拟通常使用显式但有限的电子库。这些电子库应收敛到正确的连续极限，尽管在离散化和计算成本之间存在权衡。在这里，我们研究扩展库模拟中的这种相互作用，其中弛豫会在整个系统中维持偏置或温度降。我们的分析从非相互作用极限开始，在该极限中我们对不同的离散化进行参数化，以便在平等的基础上对它们进行比较。对于多体系统，我们开发了一种方法，通过控制电流的克莱默斯翻转中的虚拟跃迁来估计最接近连续极限的弛豫。虽然有些离散化在计算电流方面更有效，但对于系统的整体状态几乎没有益处。对于多体张量网络模拟，任何收益都变得微不足道，在扫描其他数值控制时，离散化的相对性能会有所不同。这些结果表明，典型的库离散化对某些计算工具的数值成本影响很小。然而，弛豫参数的选择至关重要，我们开发的方法为有限库的最优弛豫提供了可靠的估计。
