Curvature fluctuations and the Lyapunov exponent at melting

Abstract

We calculate the maximal Lyapunov exponent in constant-energy molecular-dynamics simulations at the melting transition for finite clusters of 6--13 particles (model rare-gas and metallic systems) as well as for bulk rare-gas solids. 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 toward 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.