CURVATURE FLUCTUATIONS AND ELITE LYAPUNOV EXPONENT AT MELTING

We calculate the maximal Lyapunov exponent in constant-energy molecula r-dynamics simulations st the melting transition for finite clusters o f 6-13 particles (model rare-gas and metallic systems) as well as for bull; rare-gas solids. For clusters, the Lyapunov exponent generally v aries linearly with the total energy, but the slope changes sharply at the melting transition. In the hulk system, melting corresponds to a jump in the Lyapunov exponent, and this corresponds to a singularity i n the variance of the curvature of the potential-energy surface. In th ese systems there are two mechanisms of chaos-local instability and pa rametric instability. We calculate the contribution of the parametric instability toward the chaoticity of these systems using a recently pr oposed formalism. The contribution of parametric instability is a cont inuous function of energy in small clusters but not in the bulk where the melting corresponds to a decrease in this quantity. This implies t hat the melting in small clusters does not lead to enhanced local inst ability.