Towards anomalous diffusion with nonlinear interactions for Hamiltonian chaotic systems

A macroscopic transport equation has been derived from the underlying microscopic dynamics and a general fluctuation-dissipation relation is proposed for a microscopic system composed of the collective degrees of freedom coupled to finite intrinsic ones through a weak interaction. With the aid of numerical simulation, it is shown that there is substantial difference in correlation function and hence a difference in the statistical process between linear and nonlinear coupling interaction. It turned out that the statistical relaxation in the finite system has an anomalous diffusion and the fluctuation effects have finite correlation time.