Soft-mode dynamics in nematic liquid crystals

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Abstract
The dynamic properties of the molecular model proposed by Maier-Saupe (MS) for nematic liquid crystals are investigated. It is shown that the model predicts diffusive optic soft modes, describing nematic-order-parameter fluctuations which condense at the isotropicnematic stability limit. Since the MS Hamiltonian in its usual form does not exhibit the full symmetry of the high-temperature phase, no symmetry-recovering Goldstone mode is predicted. A rotationally invariant form of the Maier-Saupe Hamiltonian, on the other hand, predicts the existence of two different diffusive optic soft modes in the nematic phase, in addition to a doubly degenerate "magnon" mode which is the Goldstone mode of the isotropicnematic transition.