Quanta= cumulant mechanics and dynamics for multidimensional quantum many-body clusters
Quanta= cumulant mechanics and dynamics for multidimensional quantum many-body clusters
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Quanta= 多维量子多体团簇的累积力学和动力学
DOI：
10.1002/qua.24052
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发表时间：
2013
影响因子：
2.2
通讯作者：
重田育照
中科院分区：
文献类型：
--
作者：
冬木正紀;古田康一;和田昭英;美齊津文典;重田育照
我们发展了量子累积力学来处理多维量子多体团簇，包括两体相互作用，如莫尔斯势。为了评估实际计算中出现的有效电势，采用高斯拟合方法对莫尔斯电势进行近似。再现经典三维（3D）莫尔斯3 （M3）星团的总能量所需的高斯数为31，其中误差为10−6。我们将经典m3簇的结构与量子对应物的结构进行了比较，发现由于零点振动效应，量子结构具有广泛的分布。通过对累积矩阵进行对角线近似，簇的对称性从md3hto d2h开始降低。相反，原始和球面近似保持对称约束。我们还对具有两种不同稳定结构的二维m4簇进行了相同的分析，其中一种具有d3h对称，另一种具有d2h对称。在后一种情况下，当三个笛卡尔轴中的两个与集群对称轴重合时，对角线近似意外地给出了与原始近似相同的结果。当星团围绕这些轴旋转时，对角线近似的结果与原始近似的结果有偏差，并且还发现了人为的对称性破缺。我们还评价了n= 4-7范围内的高度对称小莫尔斯簇的优化结构，并与相应的经典结构进行了比较。我们发现，总能量的对角线近似和球面近似的误差都随着粒子数的增加而减小。这一事实表明，这些近似将有助于以低计算成本研究多粒子量子团簇的静态和动态特性。©2012 Wiley期刊公司
We developed the quantal cumulant mechanics for treating multidimensional quantum many‐body clusters including two‐body interaction such as the Morse potential. To evaluate an effective potential appearing in the actual calculation, a Gaussian fitting method was adopted to approximate the Morse potential. The number of the Gaussians that are required to reproduce the total energy of a classical three‐dimensional (3D) Morse 3 (M3) cluster is 31, where the error is 10−6. We compared structures of the classical M3cluster with those of quantum counterpart and found that the quantum structure have broad distribution due to zero point vibration effects. The symmetry of the cluster becomes lower fromD3htoD2hby applying the diagonal approximation to the cumulant matrices. Conversely, the original and spherical approximation holds the symmetry constraint. We also perform the same analyses on 2D M4cluster with two different stable structures, where one hasD3hsymmetry and the otherD2hsymmetry. In the latter case, the diagonal approximation accidentally gives the same results as the original one, when two of three Cartesian axes coincide with the cluster symmetric axes. When the cluster rotates with respect to these axes, the results of the diagonal approximation deviate from those by the original one and the artificial symmetry breaking is also found. We also evaluate the optimized structures of the highly symmetric small Morse clusters Mnranging fromn= 4–7 and compare with those with the corresponding classical ones. We found that the errors of both the diagonal and spherical approximations in total energy decrease with the number of particles. This fact indicates that these approximations will be useful to investigate static and dynamical properties of many‐particle quantum clusters with low computational cost. © 2012 Wiley Periodicals, Inc.