Asymptotic expansions for autocorrelation functions with Gaussian memory

Publisher Website
Google Scholar
Abstract
Mori’s integro-differential equation for equilibrium correlation functions is investigated for a Gaussian memory. For this type of memory the first four moments of the autocorrelation function are reproduced exactly. So far, however, the underlying Mori equation has only been solved numerically. In this paper analytic short-time and long-time expansions are derived by the aid of which the behavior of the autocorrelation function can be described in the whole time domain. The analysis shows that there exists a critical parameter τc which separates the regime of oscillatory from that of nonoscillatory decay of the autocorrelation function. Finally, the Gaussian memory results are compared with those of an exponential memory.