Hydrodynamic correlation functions for a nematic liquid crystal in a stationary state

We show that the general procedure developed by Fox and Uhlenbeck (Phys. Fluids 3 (1970) 1893) may be employed to describe the hydrodynamic fluctuations of a thermotropic nematic liquid crystal in equilibrium and steady states. We calculate explicitly the matrix of correlation functions for the transverse variables of a nematic film confined between two horizontal plates and subjected to a constant pressure gradient. We find that the light scattering spectrum and the intensity of the Rayleigh line are calculated from the orientation correlation function in equilibrium to first order in the pressure gradient. The shape and intensity of these lines deviate from their equilibrium values by amounts proportional to the imposed gradient, leading to an asymmetry in their height and intensity. It is shown that these effects may as large as 94.3% for a value of of the pressure gradient, suggesting that this effect might be observable.