Electron dynamics in a two-sites Hubbard model is studied using the nonequilibrium Green's function approach. The study is motivated by the empirical observation that a full solution of the integro-differential Kadanoff–Baym equation (KBE) is more stable and often accompanied by artificial damping [Marc Puig von Friesen, C. Verdozzi, and C.-O. Almbladh (2009)] than its time-linear reformulations relying on the generalized Kadanoff–Baym ansatz (GKBA). Additionally, for conserving theories, numerical simulations suggest that KBE produces natural occupations bounded by one and zero in agreement with the Pauli exclusion principle, whereas, in some regimes, GKBA-based theories violate this principle. As the first step for understanding these issues, the electron dynamics arising in the adiabatic switching scenario is studied. Many-body approximations are classified according to the channel of the Bethe–Salpeter equation in which electronic correlations are explicitly treated. They give rise to the so-called second Born, T-matrix, and GW approximations. In each of these cases, the model is reduced to a system of ordinary differential equations, which resemble equations of motion for a driven harmonic oscillator with time-dependent frequencies. A more complete treatment of electronic correlations is achieved by combining different correlation channels, with parquet theory serving as a starting point.

中文翻译：

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哈伯德二聚体的非平衡动力学

使用非平衡格林函数方法研究了两点哈伯德模型中的电子动力学。这项研究的动机是经验观察，即积分微分 Kadanoff-Baym 方程 (KBE) 的完整解更加稳定，并且通常伴有人工阻尼 [Marc Puig von Friesen、C. Verdozzi 和 C.-O. Almbladh (2009)] 比其依赖于广义 Kadanoff-Baym ansatz (GKBA) 的时间线性重新表述更重要。此外，对于守恒理论，数值模拟表明 KBE 产生以 1 和 0 为界的自然占据，与泡利不相容原理一致，而在某些体系中，基于 GKBA 的理论违反了这一原理。作为理解这些问题的第一步，我们研究绝热切换场景中出现的电子动力学。多体近似根据 Bethe-Salpeter 方程的通道进行分类，其中明确处理了电子相关性。它们产生了所谓的二阶 Born、T矩阵和GW近似。在每种情况下，模型都简化为常微分方程组，类似于具有与时间相关的频率的驱动谐振子的运动方程。以镶木地板理论为起点，通过组合不同的相关通道，可以实现对电子相关性的更完整的处理。