本课题主要研究非平衡Green函数法和Wigner分布函数法在量子输运中的应用。随着器件极小化的过程，量子输运方程的求解变得越来越重要，Green函数法和Wigner分布函数法是求解量子输运的两个重要方法。我们将研究多体Green函数到单体Green函数的过渡关系，特别是单体Green函数简单的散射描述与多体Green函数从第一性原理出发的自能项的联系，以及Green函数自能项与动理学方程散射项的联系，对不同散射描述给出统一理论框架。在原有的稳态弹道输运工作基础上考虑散射效应和瞬时效应，验证散射项的分析结果和含时问题的稳定性。对求解多体问题的GW近似方法设计改进的谱元函数，设计高效的计算方法，提高多体问题的计算效率。

This project is mainly about the application of the non-equilibrium Green function and Wigner distribution function in quantum transport. As the device shrinks to nanometer size,quantum transport models become more important for device designing. The relation of one-partical Green function with many-body Green function will be studied, especially the description of the scattering effect in Green function methods. We also care about the relation of self-enengy in frame of Green function and the scattering description in quantum kinetic model. The transient effect and the scattering effect will be added on the base of our research on ballistic and static quantum transport models. An efficient set of improved basis functions will be given for GW approximation to compute the many-body problems efficiently.