标题： 三维量子输运的空间平均非平衡格林函数方法 显示英文标题

标题： Space-averaged non-equilibrium Green's function approach for quantum transport in 3D

摘要： 非平衡格林函数（NEGF）方法为模拟介观系统中的各种现象提供了一个实用的框架。 随着电子器件的尺寸缩小到仅几纳米，基于有效质量的新三维 NEGF 实现的需求变得越来越明显。 本文扩展了我们之前开发的有限体积实现——最初用于二维薛定谔方程和泊松方程的自洽求解——为完整的三维 NEGF 框架。 我们的实现从探讨常见教科书有限差分 NEGF 实现的一些问题开始。 然后我们简洁地展示有限体积离散化如何解决几个关键的实现挑战。 重要的是，我们解释了这种离散化如何能够评估自能，从而考虑库区的影响。 通过两个例子展示了该新方法的潜在应用。 我们预计此实现将广泛适用于开放量子系统，特别是在完全三维域至关重要的情况下。 显示英文摘要

摘要： The non-equilibrium Green's function (NEGF) approach offers a practical framework for simulating various phenomena in mesoscopic systems. As the dimension of electronic devices shrinks to just a few nanometers, the need for new effective-mass based 3D implementations of NEGF has become increasingly apparent. This work extends our previous Finite-Volume implementation -- originally developed for the self-consistent solution of the Schr\"odinger and Poisson equations in 2D -- into a full 3D NEGF framework. Our implementation begins with exploring a few problems with the common textbook Finite Difference implementations of NEGF. We then concisely demonstrate how Finite-Volume discretization addresses few key implementation challenges. Importantly, we explain how this type of discretization enables evaluating the self-energies, which account for the effects of reservoirs. The potential applications of this new method are illustrated through two examples. We anticipate that this implementation will be broadly applicable to open quantum systems, especially in cases where a fully three-dimensional domain is essential.