Structural stability of simple classical fluids: Universal properties of the Lyapunov-exponent measure

A threshold for the stability of the solution of integral equations for the pair correlation function of a classical fluid can be determined from the Floquet matrix for the iterative form of the integral equation. Correspondi ngly, a measure of the structural stability of the fluid, analogous to the Lindemann ratio for a solid is provided by the Lyapunov exponent lambda tha t is related to the perturbed dynamics. The behavior of lambda as a functio n of density, temperature, interatomic potential, and closure relations for the integral equation, is analyzed and discussed. In analogy with the Lind emann parameter, we find-for the hypernetted-chain-type closures-that lambd a(T/T-inst) is "quasiuniversal," i.e., very weakly dependent on the interac tion potential, up to a temperature T/T(inst)similar to 5, where T-inst is the stability-threshold temperature. We show how this result connects the L yapunov exponent measure of the pair structure with the equation of state o f the fluid.