Numerical Evidence for Divergent Burnett Coefficients

In previous papers [Phys. Rev. A {\bf 41}, 4501 (1990), Phys. Rev. E {\bf 18}, 3178 (1993)], simple equilibrium expressions were obtained for nonlinear Burnett coefficients. A preliminary calculation of a 32 particle Lennard-Jones fluid was presented in the previous paper. Now, sufficient resources have become available to address the question of whether nonlinear Burnett coefficients are finite for soft spheres. The hard sphere case is known to have infinite nonlinear Burnett coefficients (ie a nonanalytic constitutive relation) from mode coupling theory. This paper reports a molecular dynamics caclulation of the third order nonlinear Burnett coefficient of a Lennard-Jones fluid undergoing colour flow, which indicates that this term is diverges in the thermodynamic limit.