Group theoretical treatment of classical n-time correlation functions

Abstract

The methods of group theoretical statistical mechanics are used to investigate the set of n-time correlation functions in isotropic molecular liquids and in molecular liquids subjected to external electric and magnetic fields. It is found that the group theory corroborates the results of computer simulation where these are available, both for auto- and cross-correlation functions, in the field-off and field-on equilibrium conditions. Many more elements of the time correlation functions are allowed by symmetry in the presence of fields. For the first time, the symmetry and time dependence of higher-order n-time correlation functions are investigated by group theory. This results in a great simplification of the exploratory work of the computer simulator, because the group theory clearly distinguishes between those elements that vanish for all t and those that may exist in the laboratory frame ( X, Y, Z) and the molecule-fixed frame ( x, y, z). Group theoretical statistical mechanics reveal clearly that the statistics of a molecular liquid cannot be Gaussian in general, because three-time and higher-order correlation functions exist by symmetry. These should be observable in future computer simulation. Thus we arrive at the important conclusion that group theory applied to the dynamics of molecules in the liquid state invalidates a large number of literature theories of diffusion, including all those based on the Debye concept of “rotational” diffusion. These theories should be modified accordingly.