INTEGRAL-REPRESENTATION OF EXACT-SOLUTIONS FOR THE CORRELATION TIMES OF ROTATORS IN PERIODIC POTENTIALS - DERIVATION OF ASYMPTOTIC EXPANSIONS

The derivation of asymptotic expansions from the exact solution of the three term recurrence relations arising in the study of the Brownian movement in a periodic potential is discussed. The discussion is illus trated by showing how the exact formulae for the longitudinal and tran sverse correlation times of a single axis rotator with two equivalent sites, which have been previously given as a series of products of mod ified Bessel functions, may be rendered in integral form using Watson' s integral formula for the product of two modified Bessel functions. T he method of steepest descents is applied to these solutions in order to obtain rigourous asymptotic formulae for the correlation times in t he high potential barrier limit. The analogous results for rotation in three dimensions in the Maier-Saupe potential are treated briefly.