Spin Wave Theory To The Nematic Liquid Crystal

As far as the theoretical description of the nematic liquid crystals is concerned, classical theories have been used up to now, such as L. Onsager molecular field theory, L. Landau-P. G. de Gennes theory and W. Maier-A. Saupe molecular field theory. Considering that the liquid crystals are many-body system, so many-body effect or collective excitation can have an important effect on macroscopic properties. Many quite effective methods have been developed in solid-state quantum theory by which many problems have been solved successfully. A spin wave theory is proposed in this article, it is the first time that quantum theory is applied to research the liquid crystals.Since the orientation of the molecular long axis and the angular momentum of the molecule rotating around its long axis have the same direction, operators can be introduced to research the nematic liquid crystals. Using the cell model and the Holstein-Primakoff transformation, the Hamiltonian of the system can be obtained, which has the same form as that of the ferromagnetic substance. The relation between the order parameters and reduced temperature can be gotten. It is in good agreement with the experimental results at low temperature region, the accordance is better than that of the molecular field theory and the computer simulation. At high temperature region close to the transition point, by considering the higher-order effect, theoretical values are in accordance with the experimental ones, too. That indicates the many-body effect (collective excitation) is important.