Chebyshev多项式方法求解纳米结构中量子输运的Landauer-Büttiker公式
Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
摘要：
Landauer-Büttiker公式描述了纳米结构和分子中的电子量子输运。由于例如矩阵求逆计算，对于复杂或大尺寸系统的模拟，这将是数值要求很高的。近年来，Chebyshev多项式方法由于其所涉及的矩阵运算仅为稀疏矩阵与向量的乘积，因而在量子系统的数值模拟中具有很高的并行效率，引起了人们的极大兴趣。孤立量子结构或体量子结构的物理量的Chebyshev多项式表示已经取得了许多进展。在这里，我们提出了Chebyshev多项式方法的典型电子散射问题，Landauer-Büttiker公式的纳米结构中的量子输运的电导。我们首先描述了完整的算法的基础上的标准浴核多项式方法（KPM）。然后，我们提出了两个简单但有效的改进。其中一种方法的时间消耗明显小于不使用KPM的直接矩阵计算。最后给出了一些典型的算例来说明数值计算的有效性.
英文摘要：
Landauer-Büttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations. Recently, Chebyshev polynomial method has attracted intense interests in numerical simulations of quantum systems due to the high efficiency in parallelization, because the only matrix operation it involves is just the product of sparse matrices and vectors. Many progresses have been made on the Chebyshev polynomial representations of physical quantities for isolated or bulk quantum structures. Here we present the Chebyshev polynomial method to the typical electronic scattering problem, the Landauer-Büttiker formula for the conductance of quantum transports in nanostructures. We first describe the full algorithm based on the standard bath kernel polynomial method (KPM). Then, we present two simple butefficient improvements. One of them has a time consumption remarkably less than the direct matrix calculation without KPM. Some typical examples are also presented to illustrate the numerical effectiveness.
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