On physical property tensors invariant under line groups

Abstract

The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of aninfinitenumber of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an indexnand a physical property tensor of rankm, the form of the tensor for all line group types indexed withn>mis the same, leaving only afinitenumber of tensor forms to be determined.