| 概 要 |
The behavior of molecules, clusters and nanoparticles of dielectric materials lends itself to description in terms of movement on an effective potential surface.
The surface for a system of N atoms has 3N–6 independent variables, and energy as the dependent variable, a function of the position of all the component atoms. Such a surface is incredibly complex, typically with the number of geometrically-distinct local minima depending approximately exponentially on N, but permutational symmetry increases this by a factor of N! for identical atoms. The number of saddles increases even faster with N. Describing how a system moves on such a surface is a formidable challenge for kinetics. The behavior of a collection of metal atoms is still more complex because more than one potential surface may be involved in its kinetics and dynamics. We will discuss some ways to begin to understand such dynamics by examining local behavior in the vicinity of stationary points, using local Liapunov exponents to show the extent of local regular or chaotic behavior.
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