Diffusion in Hamiltonian chaos and its size dependence

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Abstract
The diffusion process of Hamiltonian map lattice models is numerically studied. For weak non-integrability, the diffusion coefficient of the model has stretched exponential dependence on the non-integrability, which is consistent with Nekhoroshev's bound. Up to a certain size, the exponent of the stretched exponential decreases with the system size, showing that diffusion is enhanced with the increase of the size. As the size gets larger than the correlation length the exponent approaches a finite value. The diffusion coefficient of a model with global interaction is also studied. It again is enhanced with the system size.