Pandey Devashish, Oriols Xavier, Albareda Guillermo
Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, Edifici Q, 08193 Bellaterra, Spain.
Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany.
Materials (Basel). 2020 Jul 7;13(13):3033. doi: 10.3390/ma13133033.
The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows effectively separating fast and slow degrees of freedom and thus treating electrons and nuclei with different mathematical footings. Here, we consider the use of a Born-Huang-like expansion of the three-dimensional time-dependent Schrödinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a typical two-dimensional geometrical constriction and upto three orders for three-dimensional constriction.
所谓的玻恩-黄近似是从头算分子动力学中的一个基本工具，也就是说，它能有效地分离快速和慢速自由度，从而用不同的数学基础来处理电子和原子核。在此，我们考虑使用三维含时薛定谔方程的类玻恩-黄展开，以在涉及几何约束的电子输运问题中分离输运和约束自由度。由此产生的方案包括一个关于约束自由度（横向）的本征态问题，其解构成了一组用于输运自由度（纵向）的耦合一维运动方程传播的输入。对于典型的二维几何约束，该技术使用比全维模拟少一个数量级的计算资源就能达到定量精度，对于三维约束则能少三个数量级。
