Nonequilibrium dynamics of the many-body electronic excitations in atomic, molecular and model systems

近年来，阿秒物理学、分子电子学和具有原子分辨率的隧道光谱学的出现，要求在凝聚态和量子化学中发展新的理论方法。 阿秒分辨率使人们能够探测原子系统和远离平衡态的凝聚态中的电子激发。分子电子学和时间分辨扫描隧道光谱学中的时间尺度要慢得多。然而，系统被置于非平衡制度的外部施加的电压。在这两种情况下，传统的多体微扰理论（MBPT）不再有效。 密度矩阵方法、含时密度泛函理论（TDDFT）、密度矩阵重整化群（tDMRG）和非平衡绿色函数（NEGF）等理论方法都是处理这类实验条件的理论方法，我们的理论项目将集中在NEGF类方法来描述远离平衡态的原子、分子和模型系统中的电子激发动力学。该方法的选择不是任意的：i）与密度矩阵方法相比，它更容易找到满足宏观守恒律的近似; ii）它可以在一次计算中一致地描述中性和带电激发; iii）该方法可以用作通过Sham-Schlüter方程或优化的有效势（OEP）方法;（iv）与tDMFT相比，NEGF方法不局限于模型系统，在Kwong和Bonitz通过传播Kadanoff-Baym方程数值求解了均匀电子气（HEG）的两时间关联函数，Dahlen和货车Leeuwen首次求解了原子和分子系统的这些方程之后，NEGF方法从纯理论工具转变为强大的数值方法。 虽然很多的努力已经投入到测试各种近似模型系统的方法应用到现实系统是稀缺的。这个项目的目标是将这些方法推向一个实用的从头算工具，以模拟原子，分子和模型系统中的强非平衡动力学。我们计划用它来研究阿秒时间尺度上的光-物质相互作用和纳米尺度上的电子输运。

In recent years the emergence of attosecond physics, molecular electronics and tunneling spectroscopy with atomic resolution have called for the development of new theoretical methods in condensed matter and quantum chemistry. Attosecond resolution enables one to probe electronic excitations in atomic systems and in condensed matter far from equilibrium. The time scales in molecular electronics and time resolved scanning tunneling spectroscopy are much slower. However, the systems are put in the nonequilibrium regime by the externally applied voltage. In both cases the conventional many-body perturbation theory (MBPT) ceased to be valid. The hierarchy of density matrix methods, time-dependent density functional theory (TDDFT), density matrix renormalization group (tDMRG), and the nonequilibrium Green's function (NEGF) approaches are theoretical methods capable to deal with this kind of experimental conditions.Our theoretical project will focus on the NEGF class of methods to describe the dynamics of electronic excitations in atomic, molecular and model systems far from equilibrium. The choice of the method is not arbitrary: i) In comparison with the density matrix method it is easier to find approximations which fulfill macroscopic conservation laws; ii) It is possible to consistently describe both neutral and charged excitations within a single-shot calculation; iii) The method can be used as a starting point for development exchange-correlation functionals via the Sham-Schlüter equation or optimized effective potential (OEP) approach; iv) In comparison to tDMFT the method is not limited to model systems.The NEGF methodology transformed from the pure academic tool into the powerful numerical method after Kwong and Bonitz numerically found the two-time correlation functions of the homogeneous electron gas (HEG) by propagating the Kadanoff-Baym equations, and Dahlen and van Leeuwen solved for the first time these equations for the atomic and molecular systems. While a lot of efforts have been put on testing various approximations for model systems applications of the method to realistic systems are scarce. The goal of this project is to push these methods towards a practical ab initio tool to model strongly nonequilibrium dynamics in atomic, molecular and model systems. We plan to use it to study light-matter interaction on the attosecond timescale and electron transport on the nanoscale.