The physical property tensors of one-dimensional quasicrystals

According to the group representation theory, we derive the character formulae of representation-matrices of the physical property tensors for the one-dimensional (1D) quasicrystals. Based on this, we have calculated the numbers of independent components of representation-matrices for thermal expansion coefficient tensors, piezoelectric coefficient tensors and elastic constant tensors under 31 point-groups for the 1D quasicrystals. Moreover, we have deduced the particular matrix forms of these tensors under the 31 point-groups. This is an important complement of quasicrystal physical property.