论文标题
由刚性分子形成的局部各向异性分类：对称性和张量
Classifying local anisotropy formed by rigid molecules: symmetries and tensors
论文作者
论文摘要
我们考虑一个无限的体积，其中有许多相同的刚性分子，并讨论了张量中该体积对局部各向异性的描述和分类。首先，我们检查了一个刚性分子的对称性，该分子由$（3）$中的点组描述。对于$ SO（3）$中的每个点组，我们发现该组旋转下的张量不变。这些张量应为对称和无可靠的。我们写下明确的表达方式。然后选择描述局部各向异性的顺序参数作为对密度函数的平均一些不变张量。接下来，我们通过整个无限体积的对称性讨论局部各向异性的分类。在最大熵状态的意义上，可以通过顺序参数张量的值来识别此介质对称性。对于涉及不同分子对称性的某些顺序参数张量，我们给出了介质对称性的分类，其中检查了三个，四倍和多面体对称性。
We consider an infinitesimal volume where there are many rigid molecules of the same kind, and discuss the description and classification of the local anisotropy in this volume by tensors. First, we examine the symmetry of a rigid molecule, which is described by a point group in $SO(3)$. For each point group in $SO(3)$, we find the tensors invariant under the rotations in the group. These tensors shall be symmetric and traceless. We write down the explicit expressions. The order parameters to describe the local anisotropy are then chosen as some of the invariant tensors averaged about the density function. Next, we discuss the classification of local anisotropy by the symmetry of the whole infinitesimal volume. This mesoscopic symmetry can be recognized by the value of the order parameter tensors in the sense of maximum entropy state. For some sets of order parameter tensors involving different molecular symmetries, we give the classification of mesoscopic symmetries, in which the three-fold, four-fold and polyhedral symmetries are examined.
