Nonadiabatic Time Dependent Density Functional Theory and fast nonlinear dynamics of quantum many-body systems

该项目旨在开发和数值实现时间相关密度泛函理论（TDDFT）中新的非绝热近似。非绝热交换相关（xc）效应的描述是基于我们在局部拉格朗日坐标系中从共运动观测者的角度表述非平衡多体问题的最新进展。这个概念允许考虑xc记忆效应，从而克服了TDDFT中长期存在的超局部性问题。在本项目中，将以最一般的形式重新表述共动框架中的TDDFT，该形式仅使用一个基本变量-变形张量，并根据有效向量势描述xc效应。本提案的主要焦点是TDDFT的拉格朗日（几何）公式在选定模型系统中的数值实现和应用。非线性多电子动力学超越绝热近似的数值模拟将执行量子纳米结构，缺陷，和半导体表面。

The project is aimed at a development and numerical implementation of new nonadiabatic approximations in Time Dependent Density Functional Theory (TDDFT). The description of nonadiabadic exchange-correlation (xc) effects is based on our recent advances in formulating the nonequilibrium many-body problem from the point of view of a co-moving observer in a local Lagrangian frame. This concept allows to account for the xc memory effects and thus to overcome a long standing problem of ultranon-locality in TDDFT. In this project TDDFT in a co-moving frame will be reformulated in the most general form, which operates with only one basic variable - the deformation tensor, and describes xc effects in terms of an effective vector potential. The main focus of the present proposal is a numerical implementation and applications of the Lagrangian (geometric) formulation of TDDFT to selected model systems. Numerical simulations of nonlinear many-electron dynamics beyond adiabatic approximation will be performed for quantum nanostructures, defects, and surfaces of semiconductors.