Origin of diffusion in Hamiltonian dynamics

Without invoking any kind of ''loss of memory'' hypothesis, a diffusion equation is derived for the Hamiltonian dynamics defined by H=p(2)/2+(K/4 pi(2))Sigma(m=-M)(M) cos(q-mt+phi(m)), where the phi(m)s are fixed random phases. The key point of the derivation is a property of locality for the waves inducing transport. Using perturbation theory, it is shown that only waves whose phase velocities satisfy \m-p(t)\less than or equal to alpha(K/4 pi(2))(2/3), where alpha is a constant, approximately 5, play a relevant role for the statistical properties of the dynamics. This implies scaling properties for the dynamics, and leads to the understanding of the origin of force decorrelation and of diffusion, and to the prediction of their occurrence in time. Moreover, the convergence of the diffusion coefficient to its quasilinear value when K --> infinity is shown, and is interpreted as the consequence of the crossover between two regimes of decorrelation that are of different natures. (C) 1997 American Institute of Physics.