Curvature Fluctuations and the Lyapunov exponent at Melting

We calculate the maximal Lyapunov exponent in constant-energy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare–gas and metallic systems) as well as for bulk rare– gas solid. For clusters, the Lyapunov exponent generally varies linearly with the total energy, but the slope changes sharply at the melting transition. In the bulk system, melting corresponds to a jump in the Lyapunov exponent, and this corresponds to a singularity in the variance of the curvature of the potential energy surface. In these systems there are two mechanisms of chaos – local instability and parametric instability. We calculate the contribution of the parametric instability towards the chaoticity of these systems using a recently proposed formalism. The contribution of parametric instability is a continuous function of energy in small clusters but not in the bulk where the melting corresponds to a decrease in this quantity. This implies that the melting in small clusters does not lead to enhanced local instability.