论文标题
将任意的几何相关性包括到一维时间依赖性的schrödinger方程中
Including arbitrary geometric correlations into one-dimensional time-dependent Schrödinger equations
论文作者
论文摘要
在Ab-Initio分子动力学的背景下，所谓的Born-huang ansatz是一种基本工具，即它允许有效地将快速和慢的自由度分开，从而在不同的数学基础上处理电子和核。在这里，我们考虑使用三维时间依赖性的schrödinger方程的临床样扩展，以分离涉及几何限制的电子传输问题中的传输和限制自由度。最终的方案由限制自由度（横向方向上）的特征状态问题组成，其解决方案构成了传播一组耦合的自由程度运动的耦合一维运动方程的输入（在纵向方向上）。该技术使用顺序的计算资源少于原型二维收缩的整体模拟来实现定量准确性。
The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at 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 prototypical two-dimensional constriction.
