A memory expansion method was presented for macroscopic transport coefficients such as the collective and tracer diffusion coefficients. Successive terms in the expansion for collective diffusion described a rapidly decaying memory of the center-of-mass motion; thus leading to rapid convergence during numerical estimations. In the case of tracer diffusion, an expansion of similar form was obtained which contained terms that described memory effects in single-particle motion. The above coefficients were evaluated for 3 strongly-interacting surface systems, by using Monte Carlo simulation, and for a simple model diffusion system, by using molecular dynamics methods. In the case of collective diffusion, it was shown that the numerical method provided an acceleration of some 2 orders of magnitude in computation time, as compared with standard methods. In the case of tracer diffusion, the acceleration was not quite as great. Studies which were performed by using the memory expansion method provided information on the nature of memory effects in diffusion, and the results hinted at a non-trivial power-law behavior of memory terms at intermediate times.

Memory Expansion for Diffusion Coefficients S.C.Ying, I.Vattulainen, J.Merikoski, T.Hjelt, T.Ala-Nissila: Physical Review B, 1998, 58[4], 2170-8