两种约化密度矩阵重构方法的理论分析

Theoretical Analysis of Two Reconstruction Schemes of Reduced Density Matrices

利用Harris模型，详细分析了Mazziotti提出的重构方法和Chen提出的一种由低阶约化密度矩阵重构高阶约化密度矩阵的系统方法（Sciencein China B，2006，49：402）的差异．如果忽略Mazziotti方法中的^3△M、^4△M和Chen方法中的^3△M、^4△M计算结果显示两种方法的计算误差相近．更好的近似是只忽略四级项^4△M、^4△M而三级项由相应的四级项通过简缩来计算．采用Mazziotti方法计算出来的有些近似值和精确值连正负号都不同，而用Chen方法计算出来的近似值和精确值不仅正负符号一致，而且数值大小也很接近．

The effectiveness of the approach for systematical reconstruction of higher order reduced density matrices with lower order ones, which was developed by Chen （Science in China B, 2006, 49： 402）, was compared theoretically with that of Mazziotti＇s method through Harris model. In the case of omitting the cumulant terms ^3△M,^4△M in the latter and the normal product terms ^3△M,^4△M in the former, it was found that the errors from both approaches were comparable. As a better approximation, if only fourth-order terms ^4△Mand^4△M in both methods are neglected whereas the third-order terms ^3△M and ^3△ are computed from their corresponding fourth-order terms ^4△M and^4△M respectively through contractions, the results calculated with Chen＇s approach not only have the correct signs but also are very close to the exact normal products ^3△ whereas some of the results calculated with Mazziotti＇s method do not even have the correct signs with respect to the exact cumulants ^3△M.