论文标题
刚性分子之间相互作用内核的对称性扩展
Symmetry-consistent expansion of interaction kernels between rigid molecules
论文作者
论文摘要
我们讨论了各向异性刚性分子之间相互作用内核的扩展。扩展将相关的定向变量分解，以便将其用于得出宏观模型。考虑了两种类型的对称性。首先，我们检查相互作用群集的对称性，包括整个群集的翻译和旋转，以及集群中的标签置换。扩展由对称的无纹状体张量表示，并确定线性独立的项。然后，我们研究以$ O（3）$中的点组为特征的分子对称性。正确的旋转确定可以出现哪些对称的无纹状体张量。不当旋转将这些张量分解为两个子空间，并确定如何耦合两个子空间中的张量。对于每个点组，我们确定两个子空间，以便建立与点组一致的扩展。
We discuss the expansion of interaction kernels between anisotropic rigid molecules. The expansion decouples the correlated orientational variables so that it can be utilized to derive macroscopic models. Symmetries of two types are considered. First, we examine the symmetry of the interacting cluster, including the translation and rotation of the whole cluster, and label permutation within the cluster. The expansion is expressed by symmetric traceless tensors, and the linearly independent terms are identified. Then, we study the molecular symmetry characterized by a point group in $O(3)$. The proper rotations determine what symmetric traceless tensors can appear. The improper rotations decompose these tensors into two subspaces and determine how the tensors in the two subspaces are coupled. For each point group, we identify the two subspaces, so that the expansion consistent with the point group is established.
