  Time correlation functions in the Lebwohl-Lasher model of nematic liquid
crystals are studied using theory and molecular dynamics simulations. In
particular, the autocorrelation functions of angular momentum and nematic
director fluctuations are calculated in the long-wavelength limit. The
constitutive relations for the hydrodynamic currents are derived using a
standard procedure based on non-negativity of the entropy production. The
continuity equations are then linearized and solved to calculate the
correlation functions. We find that the transverse angular momentum
fluctuations are coupled to the director fluctuations, and are both
propagative. The propagative nature of the fluctuations suppress the
anticipated hydrodynamic long-time tails in the single-particle autocorrelation
functions. The fluctuations in the isotropic phase are however diffusive,
leading to $t^{-d/2}$ long-time tails in $d$ spatial dimensions. The Frank
elastic constant measured using the time-correlation functions are in good
agreement with previously reported results.
