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In general, nonexponential relaxation can result either from a heterogeneous (superposition of different exponential processes) or a homogeneous scenario (identical intrinsically nonexponential processes). In the present paper for the first time a strict definition of both scenarios is formulated. A procedure is presented which allows to estimate the heterogeneous and homogeneous contributions to the nonexponentiality, i.e., the type of relaxation, from comparing a two-time and a three-time correlation function. On this basis the type of relaxation is calculated analytically for the Rouse model. The relaxation of the Rouse model turns out to be mainly homogeneous. Furthermore, the type of relaxation is calculated for the dynamics of a simulated polymer melt above the glass transition. The polymer model used in this work is the well-known bond fluctuation model. For large lengthscales and high temperatures the relaxation of the polymer melt is mainly homogeneous in quantitative agreement with the Rouse model. However, for short length scales and/or low temperatures the dynamics of the polymer melt contains significant heterogeneous contributions. This is a direct indication of the relevance of local intermolecular interactions for the polymer dynamics. Furthermore the fluctuations within the heterogeneous rate distribution are analyzed. The time scale of fluctuations turns out to be of the same order as the relaxation process itself.
Heuer et al. (Tue,) studied this question.