Transport Coefficients from Projection Operators in the Time Correlation Function Formalism.

Previous work by Kawasaki and Oppenheim [Phys. Rev. 136, A1519 (1964)] has used a binary collision expansion of the resolvent in the time correlation function . This has necessitated a resummation to obtain a finite transport coefficient. The present work compares their results with the expressions derived via the Boltzmann equation, that has been used by Rainwater and Friend [Phys. Rev. A 36, 40 (1987)] for the detailed comparison with experiment using realistic intermolecular potentials. The projection operator approach avoids the resummation of divergent terms and expresses the inverse of the transport coefficient in terms of their corresponding memory function. It is at this stage that a binary collision expansion is made. At low densities, the result is shown to be exactly equivalent to the Boltzmann equation derived transport coefficient. At higher densities both kinetic and potential contributions to the flux are involved. Separate projection operators are required for the two contributions and the subsequent binary collision expansion of the resulting combination of resolvents leads directly to an expression for the first order density correction to the transport coefficient.