Comparison of the Tokuyama–Mori type projection-operator method to that of Mori type near the glass transition

Two types of projection-operator methods, Mori type and Tokuyama–Mori type, are tested for studying the slow dynamics of a single particle in complex systems near the glass transition. From a unified point of view based on the mean-field theory recently proposed by the present author, the molecular- and Brownian-dynamics simulations and the corresponding solutions of the mode-coupling theory developed by employing Mori-type formalism are compared consistently. Disagreement is found for the mean-square displacements in β stage. Thus, validity of both types is fully investigated near the glass transition from a new standpoint.