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Time-dependent density functional theory of open quantum systems in the linear-response regime

机译：线性响应系统中开放量子系统的时变密度泛函理论

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摘要

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C~2 atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Grling-Levy perturbation theory is calculated.
机译：时变密度泛函理论（TDDFT）最近已得到扩展，以描述根据量子主方程在非unit动力下演化的多体开放量子系统。在主方程法中，由于周围环境对电子自由度的松弛和移相，电子激发光谱变宽和移动。在本文中，我们为在主方程下演化的多体电子系统开发了TDDFT线性响应理论（LR-TDDFT），从而产生了更宽的激发光谱。这是通过将相互作用的开放量子系统映射到非相互作用的开放Kohn-Sham系统上来完成的，从而产生正确的非平衡密度演化。对于Redfield主方程，推导了一个类似于通常LR-TDDFT的Casida方程的伪特征值方程，从而产生了复能和兰姆位移。作为简单的演示，我们通过将电磁场真空视为光子浴来计算包括自然线宽在内的C〜2原子的光谱。分析了绝热交换相关核的性能，并基于Grling-Levy扰动理论计算了裸露Kohn-Sham线宽的一阶频率相关校正。

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