核响应函数的实时Kadanoff-Baym方法
Real-time Kadanoff-Baym approach to nuclear response functions
摘要：
本文用时间演化的两次格林函数实时计算了正常密度对称核物质的线性密度响应函数。特别令人感兴趣的是相关性的影响。因此，该系统最初的时间演化与碰撞项计算在一个直接玻恩近似，以及与完整的（RPA）环求和，直到完全相关。然后施加外部时间相关电位。记录随后的密度波动以计算密度响应。这种方法以前被邝和Bonitz用于研究相关电子气中的等离子体振荡。能量加权求和规则的响应函数是通过使用保存的自能量插入，然后生成完整的顶点函数的方法来保证。这些也可以通过求解贝特-萨尔彼得方程来计算，就像在以前的一些作品中所做的那样。（一阶）平均场来自动量相关（非局部）相互作用，而$2^{nd}$阶自能使用由高斯\it局部\rm势给出的粒子-空穴两体有效（或“剩余”）相互作用来计算。我们提出了数值结果的响应函数$S(ω,q_0)$的$q_0=0.2,0.4$和$0.8 {\rm fm}^{-1}$。与核子是不相关的，即只有一阶平均场包括在内，“HF+RPA”近似。我们简要地讨论了我们的工作的关系与朗道准粒子理论应用于核系统的Sjöberg和追随者使用的方法开发的巴布和布朗，特别强调的“诱导”的相互作用。
英文摘要：
Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Green's functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation as well as with full (RPA) ring-summation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in some previous works. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while $2^{nd}$ order self-energies are calculated using a particle-hole two-body effective (or 'residual') interaction given by a gaussian \it local \rm potential. We present numerical results for the response function $S(ω,q_0)$ for $q_0=0.2,0.4$ and $0.8 {\rm fm}^{-1}$. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included, the 'HF+RPA' approximation. We briefly discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Sjöberg and followers using methods developped by Babu and Brown, with special emphasis on the 'induced' interaction.
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