物理学进展

物理学进展 ›› 2019, Vol. 39 ›› Issue (4): 119-136.

• •    下一篇

一种含时量子输运的理论和应用

程霄，谢航   

  • 发布日期:2020-10-12

Time-Dependent Quantum Transport: Theory and Application量子输运；含时；运动方程；非平衡格林函数理论；复数吸收势；自能

Cheng Xiao, Xie Hang   

  • Published:2020-10-12

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摘要： 含时量子输运研究的是开放体系中的电子波的演化问题。这类问题，由于电极耗散等外界 环境的影响，中心体系内的电子运动受外场驱动时，其运动状况不光取决于当下时刻，还和过去 一段时刻的历史状况求和相关。这是一种非马尔科夫过程，数学上也比较难以求解。 本文以非平衡格林函数为基础，详细介绍了一类新的求解含时量子输运的方法：密度矩阵 的运动方程方法。这种方法理论上步骤清晰，易于数值计算，特别是可以推广到较大体系的计 算。另外，本文还介绍了其他一些含时输运方法，并举例说明了这类含时输运理论的应用，如石 墨烯等二维材料中的瞬态电流，有多体作用的开放量子点体系中的电子动力学等。

关键词: 量子输运；含时；运动方程；非平衡格林函数理论；复数吸收势；自能

Abstract: Time-dependent quantum transport (TDQT) theory researches the electron wave evolution in the open systems. Due to the dissipation of leads or other environmental effects, the electrons behavior in the central region does not only depends on the instant external fields, but also on the historical accumulations in some past period. This is a non-Markov process, which is some complicated to be solved in mathematics. In this paper, we introduce a new type of TDQT theory: density-matrix equation of motion (DM-EOM) method in detail. It is based on the non-equilibrium Green’s function (NEGF) theory. This method has clear calculation schemes and it is easy for the numerical implementation, especially for the large systems. We also introduce some other QDTD methods and their applications. For example, the transient current in graphene and other 2D materials, the electron dynamics in open quantum dots with the many-body interactions.

Key words: quantum transport; time-dependent; equation of motion; non-equilibrium Green’s function theory; complex absorbing potential; self-energy