Correlated quantum many‐particle systems out of equilibrium are of high interest in many fields, including correlated solids, ultracold atoms, or dense plasmas. Accurate theoretical description of these systems is challenging both, conceptionally and with respect to computational resources. A quantum fluctuations approach is recently presented, which is equivalent to the nonequilibrium GW approximation that promises high accuracy at low computational cost. The method exhibits process time scaling that is linear in the number of time steps, like the G1–G2 scheme, however, at a much reduced computer memory cost. In a second publication, this approach is extended to the two‐time exchange–correlation functions and the dynamic density response properties. Herein, the properties of this approach are analyzed in more detail. The physical meaning of the central approximation, the quantum polarization approximation, is established. It is demonstrated that the method is equivalent to the Bethe–Salpeter equation for the two‐time exchange–correlation function when the generalized Kadanoff–Baym ansatz with Hartree–Fock propagators is applied.

中文翻译：

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二次量子涨落方法及其与 Bethe-Salpeter 方程的关系

失去平衡的相关量子多粒子系统在许多领域都引起了人们的高度兴趣，包括相关固体、超冷原子或致密等离子体。这些系统的准确理论描述在概念上和计算资源方面都具有挑战性。最近提出了一种量子涨落方法，相当于非平衡态GW以低计算成本保证高精度的近似。该方法表现出与时间步数成线性关系的处理时间缩放，就像 G1-G2 方案一样，但计算机内存成本大大降低。在第二篇出版物中，这种方法被扩展到两次交换相关函数和动态密度响应属性。在此，更详细地分析该方法的特性。建立了中心近似、量子极化近似的物理意义。结果表明，当应用带有 Hartree-Fock 传播器的广义 Kadanoff-Baym ansatz 时，该方法等效于两次交换相关函数的 Bethe-Salpeter 方程。