Information content of multitime correlation functions for the interpretation of structural relaxation in glass-forming systems

In recent experiments four-time correlation functions have been systematically measured for a polymer near the glass transition via methods of multidimensional NMR [A. Heuer et al., Phys. Rev. Lett. 75, 2851 (1995)]. In this paper a theoretical analysis of the information content of multitime correlation functions is presented. Having in mind a heterogeneous distribution of relaxation rates, it is demonstrated that multitime correlation functions contain information about temporal fluctuations within the heterogenous distribution. If the relaxation rate distribution is bimodal, the additional information content of the four-time correlation function as compared to the two-time correlation function is given by the exchange rate between both dynamical states. More generally, for arbitrary rate distributions the additional information content of multitime correlation functions can be, to a good approximation, expressed by a single dimensionless parameter $Q$. This parameter is a measure for the fluctuations within the heterogeneous distribution. It is denoted rate memory parameter. It is argued that its value is related to the cooperativity of the dynamics.