Rotational diffusion of uniaxial probes in biaxial liquid crystal phases

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Abstract
We discuss the reorientation of a cylindrically symmetric probe in a biaxial orthorombic medium, such as a biaxial nematic. We write down and solve for the first time the rotational diffusion equation for a rod-like or disc-like uniaxial probe reorienting in a medium of biaxial symmetry. We calculate first and second rank correlation functions both in the uniaxial and biaxial phase, giving the possibility of following the evolution of dynamic observables of interest (e.g. spectral densities) through the uniaxial–biaxial phase transition. Nonperturbative and approximate analytical solutions are provided.