Theory of non-equilibrium Green's function (NGF) provides a practical framework for studying quantum many-body systems out of equilibrium. Extending the previous mean field approach developed for nuclear systems in one dimension with NGF, we introduce isospin degrees of freedom to the Green's functions and incorporate short-range two-body interactions in the second-order self-consistent approximation to correlations, which represents the scattering of momentum orbitals in the Born approximation. We discuss the preparation of a finite nuclear system and examine the impact of correlations on the ground state. We also excite a finite symmetric nuclear system to oscillate in an isovector dipole mode and explore the dissipation effects in the oscillation. Finally, we demonstrate how to boost a slab to a constant and stable motion in a box, based on Galilean covariance of the theory. The studies in this paper lay the ground for the future exploration of collisions of correlated nuclear systems in one dimension.

中文翻译：

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非平衡格林函数理论中一维相关核系统的动力学

非平衡格林函数理论 (NGF) 为研究非平衡量子多体系统提供了实用的框架。使用 NGF 扩展先前为一维核系统开发的平均场方法，我们将同位旋自由度引入格林函数，并将短程双体相互作用纳入相关性的二阶自洽近似中，这表示Born 近似中动量轨道的散射。我们讨论了有限核系统的制备并检查了相关性对基态的影响。我们还激发有限对称核系统以等向量偶极子模式振荡并探索振荡中的耗散效应。最后，我们演示了如何将平板提升到盒子中的恒定和稳定运动，基于该理论的伽利略协方差。本文的研究为未来探索一维相关核系统碰撞奠定了基础。