ANALYTICAL SOLUTION OF MORIS EQUATION WITH HYPERBOLIC SECANT MEMORY

The equation of motion of the auto-correlation function has been solve d analytically using a hyperbolic secant form of the memory function. The analytical result obtained for longtime expansion together with sh ort-time expansion provides a good description over the whole time dom ain as judged by a comparison with the numerical solution of the Mori equation of motion. We also find that the time evolution of the auto-c orrelation function is determined by a single parameter tau which is r elated to frequency sum rules up to fourth order. The autocorrelation function has been found to show simple decaying or oscillatory behavio ur depending on whether the parameter tau is greater than or less than some critical value. Similarities as well as differences in the time evolution of the auto-correlation have been discussed for exponential, hyperbolic secant and Gaussian approaches of the memory function.