论文标题
通过基于路径积分的重要性采样方法计算量子相关函数
Computing quantum correlation functions by Importance Sampling method based on path integrals
论文作者
论文摘要
基于广义Feynman-KAC方法的重要性采样方法已用于计算许多在零和有限温度下的许多身体系统的量子相关函数的量子观测值的平均值。具体而言，期望$ \ langle r_i^n \ rangle $，$ \ langle r_ {ij}^n \ rangle $，$ \ langle r_i^{ - n} \ n} \ rangle $ and $ \ langle r_ {ij}^{ij}^{ij}^{ - 矩阵，分区函数，内部能量和量子谐波振荡器系统的特定热量与这些数量的最佳非派别值相吻合。尽管最初的结果是概括的，但需要进行更多的实验，以改善其他现有的数值结果，而不是化学精度，特别是对于锂和铍的最后两个特性。此外，还需要做更多的工作来改善有限温度计算的试验功能。
An importance sampling method based on Generalized Feynman-Kac method has been used to calculate the mean values of quantum observables from quantum correlation functions for many body systems both at zero and finite temperature. Specifically, the expectation of $\langle r_i^n\rangle$, $\langle r_{ij}^n\rangle$, $\langle r_i^{-n}\rangle$ and $\langle r_{ij}^{-n}\rangle$ for the ground state of the lithium and beryllium and the density matrix, the partition function, the internal energy and the specific heat of a system of quantum harmonic oscillators are computed, in good agreement with the best nonrelativistic values for these quantities. Although the initial results are encouarging, more experimentation will be needed to improve the other existing numerical results beyond chemical accuracies specially for the last two properties for lithium and beryllium. Also more work needs to be done to improve the trial functions for finite temperature calculations.
