Diffusion in symplectic maps

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Abstract
The characteristic function method is used to obtain the diffusion tensor for symplectic maps. At lowest order the quasilinear result is obtained, and a series in higher-order correlations is developed. Comparison of the theory to numerical experiments is given using a four-dimensional example of Froeschlé. The experiments agree well with the theory for moderately large parameters. Arnol’d diffusion for the ‘‘thick-layer’’ case is discussed. It is shown that the short-time correlations in one canonical plane affect the diffusion in the other plane even in the limit of zero coupling. Accelerator modes exist for the Froeschlé example and cause divergences in the diffusion, but these only appear when the accelerating region is included in the ensemble.