Time correlation functions of one-dimensional rotational Brownian motion in an $n$-fold periodic potential

Time correlation functions (TCF) of one-dimensional rotational brownian motion of classical top in $n$-multiple periodic potential are investigated on the basis of the solution of the modified equation of rotational diffusion which takes into account approximately the inertial effects. Explicit expressions for TCF are obtained in the limiting cases of large and small barriers. It is shown that the model of free rotational diffusion is valid when the value of the ratio of the barrier height to mean heat energy is less than one, while the hopping model is valid when this value is larger than three. Connection between the correlation time, the height of the rotation barrier and the friction coefficient characterizing influence of the medium is obtained. The results obtained are applied to the problem of calculating the TCF for translational motion of admixture atom in a crystal and to some other problems.