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 lambda that is related to the perturbed dynamics. The behavior of lambda 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 lambda(T/T(inst)) is "quasiuniversal," i.e., very weakly dependent on the interaction potential, up to a temperature T/T(inst) approximately 5, where T(inst) 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.
Malescio
G
Istituto Nazionale per la Fisica della Materia, Unita di Ricerca di Messina, Contrada Papardo, 98166 Messina, Italy and Dipartimento di Fisica, Universita degli Studi di Messina, Contrada Papardo, 98166 Messina, Italy.
Giaquinta
PV
Rosenfeld
Y