Higher-order quasilinear approximations for the propagator of the Kramers equation

We present a systematic procedure for constructing higher-order quasilinear approximations for the propagator of the Klein-Kramers equation describing the motion of a Brownian particle in a general force field. Its key points are splitting the full force field into a linear contribution and an anharmonic correction, replacing the underlying Langevin equations by difference equations and solving these equations iteratively. An accurate single step propagator is then derived in terms of known statistical properties of the noise terms. Its use in a path integral shows this approach to be advantageous over a Taylor series expansion for the propagator recently derived employing standard techniques.