The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so-called stochastic mean-field phase-space approach, where the complex dynamics of interacting fermions is replaced by a statistical average of mean-field like trajectories is able to grasp some correlations beyond the mean-field. We explore the possibility to use alternative equations of motion in the phase-space approach. Guided by the BBGKY hierarchy, equations of motion that already incorporate part of the correlations beyond mean-field are employed along each trajectory. The method is called hybrid phase-space because it mixes phase-space techniques and the time-dependent reduced density matrix approach. The novel approach is applied to the one-dimensional Fermi–Hubbard model. We show that the predictive power is improved compared to the original stochastic mean-field method. In particular, in the weak-coupling regime, the results of the HPS theory can hardly be distinguished from the exact solution even for long time.

中文翻译：

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结合相空间和时间相关的简化密度矩阵方法来描述相互作用的费米子的动力学

将相空间方法应用于多体相互作用系统的可能性可以以降低的数值成本提供相关性的准确描述。例如，所谓的随机平均场相空间方法，其中相互作用的费米子的复杂动力学被平均轨迹（如轨迹）的统计平均值所取代，它能够掌握超出平均场的一些相关性。我们探索在相空间方法中使用替代运动方程的可能性。在BBGKY层次结构的指导下，沿着每个轨迹采用的运动方程已经包含了超出平均场的部分相关性。该方法称为混合相空间，因为它混合了相空间技术和与时间有关的降低密度矩阵方法。这种新颖的方法被应用于一维费米－哈伯德模型。我们表明，与原始的随机平均场方法相比，预测能力得到了提高。特别是在弱耦合状态下，即使很长时间，也很难将HPS理论的结果与精确的解决方案区分开。