含时密度泛函理论中的generator坐标方法：简化记忆
The generator coordinate method in time-dependent density-functional theory: memory made simple
摘要：
生成坐标（GC）方法是一种求解量子多体问题的变分方法，其中相互作用的多体波函数被构造为包含变形参数的辅助哈密顿量的本征态（通常是非正交的）的叠加。本文提出了一种含时GC方法的扩展，作为改进含时密度泛函理论（TDDFT）中交换相关（XC）势的现有近似的新方法。随时间变化的GC方法被证明是一个概念上和计算上简单的工具，以建立任何现有的绝热XC潜力的记忆效应。作为一个例子，该方法被应用到驱动的两个相互作用的电子在谐振势（胡克原子）的参数振荡。它表明，适当选择的时间相关的发电机坐标结合绝热局域密度近似再现精确的线性和非线性双电子动力学相当准确，包括功能相关的双激发，不能被捕获的TDDFT在绝热近似。
英文摘要：
The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.
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