Quasilinear diffusion for the chaotic motion of a particle in a set of longitudinal waves

The rigorous analytical calculation of the diffusion coefficient is performed for the chaotic motion of a particle in a set of longitudinal waves with random phases and large amplitudes (~ A). A first step proves the existence of a quasilinear diffusion on a time scale ~ A^{-2/3} \ln A. A second step uses this property to extend the result to asymptotic times by introducing the conditional probability distribution of position and velocity of an orbit at a given time when they are known at a previous time.