Diffusive Limit of the Lorentz Model with a Uniform Field Starting from the Markov Approximation

#### K. Ravishankar, L. Triolo

1999, v.5, №4, 385-421

ABSTRACT

We study the motion of a charged particle moving under the influence of a uniform field in the $x_1$ direction in ${\ R}^d$. At exponential times with a parameter proportional to the instantaneous speed the direction of motion of the particle is randomized while the speed is unchanged. This process describes the motion of a tracer particle in the Lorentz model with uniform field in the Boltzmann - Grad limit. We prove the existence of the diffusive limit of this random flight process with field for each value of initial energy, and characterize it using the martingale problem method. We obtain the diffusion and drift coefficients as functions of the initial energy.

Keywords: diffusion,diffusive limit,Lorentz model,martingale problem