Renormalised canonical perturbation theory for stochastic propagators

A canonical transformation which removes the coherent oscillatory motion of a particle in a stochastic potential (the renormalised oscillation-centre transformation) is constructed by a new classical perturbation method using Lie operators and Green function techniques. A frequency and wavevector dependent particle-wave collision operator is calculated explicitly for stationary, homogeneous electrostatic turbulence in the short wavelength limit. The width of the resonance is proportional to the one-third power of the quasilinear diffusion coefficient, in agreement with Dupree's result (1966). However the k dependence is quite different from that expected from a simple Wiener process model. At large k spatial diffusion dominates over velocity diffusion in sharp contrast with previous theories.