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

该项目旨在发展和数值实现含时密度泛函理论(TDDFT)中新的非绝热近似。对非绝热交换关联(XC)效应的描述是基于我们在局域拉格朗日标架中从共同运动的观察者的观点来描述非平衡多体问题的最新进展。这一概念允许解释XC存储效应，从而克服了TDDFT中长期存在的超局域性问题。在这个项目中，同动坐标系中的TDDFT将被重新表述为最一般的形式，它只与一个基本变量-形变张量一起工作，并以有效矢量势的形式描述XC效应。本建议的主要重点是TDDFT的拉格朗日(几何)公式的数值实施和在选定的模型系统中的应用。我们将对半导体的量子纳米结构、缺陷和表面进行超出绝热近似的非线性多电子动力学的数值模拟。

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.