Hydrodynamic theory of biaxial nematics

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Abstract
Biaxial nematics are usually regarded as characterized by a symmetric, traceless tensor having three different eigenvalues. It is argued that this definition is too restrictive and that a natural extension would embrace any system that breaks all three rotational symmetries while preserving translational invariance. That is, biaxial nematics need not have orthorhombic symmetry, but may be triclinic, hexagonal, cubic, or even isotropic. A non-linear hydrodynamic theory is presented which emphasizes the fundamental similarities between the different biaxial nematics and clarifies the changes in the static and dynamic behavior as the discrete symmetries vary. The Goldstone modes of any biaxial nematics are identified as two pairs of orbital waves with a complex, and one orbital diffusion with a purely imaginary, dispersion relation. If the longitudinal and transverse variables decouple, it is the longitudinal rotation angle that diffuses.

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