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. Correspondingly, a measure of the structural stability of the fluid, analogous to the Lindemann ratio for a solid, is provided by the Lyapunov exponent λ that is related to the perturbed dynamics. The behavior of λ as a function of density, temperature, interatomic potential, and closure relations for the integral equation, is analyzed and discussed. In analogy with the Lindemann parameter, we find - for the hypernetted-chain-type closures - that λ (T/Tinst) is "quasiuniversal," i.e., very weakly dependent on the interaction potential, up to a temperature T/Tinst∼5, where Tinst is the stability-threshold temperature. We show how this result connects the Lyapunov exponent measure of the pair structure with the equation of state of the fluid.