Lattice model for translational and rotational motions based on generalised diffusion equations: I. General formalism

A simple lattice model based on generalised diffusion equations and Gaussian statistics, aimed at describing diffusive translational and rotational motions, is presented. It is shown that it allows the generation of correlation functions relevant to spectroscopic techniques that are very similar to those experimentally observed in a large variety of complex systems. For some ranges of values of the model parameters, these functions, which can be expressed in closed mathematical forms, can be approximately represented by the sum of two exponentials or by “stretched" exponentials.