Non-Markovian probability density functions with applications to itinerant oscillator models

Abstract

Starting from the linear Mori-Kubo generalized Langevin equation, conditional probability density functions are derived for independent dynamical variables of a general system under the action of (non-markovian) gaussian force or torque. The special techniques developed by Adelman (1976, 1977) for brownian oscillators are here extended to the general case. As applications of the general theory, angular momentum and orientational probability density functions are computed for models of molecular rotation in fluids. The rotational dynamics of each molecule is described by an itinerant oscillator/librator. The periodicity of spatial orientation is treated in terms of wrapped distributions, and hence the planar-reorientational counterpart of the translational self van Hove function is derived. It is shown that both momentum and orientational probability density functions can exhibit widely varying time-decay properties, which are directly interpretable in terms of the structure and dynamics of the molecular fluid represented.