Helsinki Institute of Physics and Laboratory of Physics,
Helsinki University of Technology, Espoo, Finland
Department of Physics, Brown University, Providence RI 02912
I will review recent progress in developing methodology for the evaluation of tracer and collective diffusion coefficients through numerical simulations for cases, where many-particle interaction effects are dominant. The first approach is called the Dynamical Mean Field (DMF) theory, and it expresses the diffusion coefficients in a form where they are proportional to the local jump rate . This makes it numerically very efficient to study surface diffusion, and local jump rates may also be measured experimentally. The main approximation in the DMF theory is the neglect of memory effects. We have tested the DMF theory for a variety of strongly interacting systems, and find that it gives a very good approximation for the temperature and concentration dependence of collective diffusion. In the case of tracer diffusion where memory effects are more pronounced, the DMF theory is less accurate quantitatively [1,2].
To improve on the DMF theory, we have developed a memory expansion for the diffusion coefficients . This theory is formally an exact decomposition of the relevant autocorrelation functions in terms of successive terms containing all the memory effects. These terms are particularly easy to evaluate through computer simulations. In addition to diffusion coefficients, the method can be generalized to study other transport coefficients. The theory has been tested for strongly interacting systems in the case of surface diffusion, and it makes it possible to obtain very accurate values of the diffusion coefficients with up to about two orders of magnitude reduction in computer time as compared to the standard methods. Through the method it is also possible to study the behavior of the memory functions corresponding to the generalized Langevin equations for tracer and collective diffusion, respectively.
*Work done in collaboration with T. Hjelt, J. Merikoski, I. Vattulainen, and S. C. Ying.