Asymptotic behavior of orientation and angular-velocity correlation functions for a fluid of linear molecules

Expressions for the asymptotic behavior of the angular-velocity and orientation correlation functions for a fluid of linear molecules are derived by a microscopic calculation based on the generalized Langevin equation. The previously obtained $t^{\frac{-5\mathrm{}}{2}}$ decay of the angular-velocity autocorrelation function is confirmed, but a somewhat more general expression for the coefficient of this decay is obtained. The vector-orientation autocorrelation function, on the other hand, is found to decay as $t^{\frac{-7\mathrm{}}{2}}$ for long times. This result, which is based on a direct calculation of the correlation function, is in disagreement with hydrodynamic results which conjecture a $t^{\frac{-5\mathrm{}}{2}}$ decay.