Lévy walks and generalized stochastic collision models

A stochastic collision model is studied in which a test particle of a mass [Formula Presented] collides with bath particles of another mass [Formula Presented] If the distribution of time intervals between the collisions is long tailed, the relaxation of momentum of the test particle is algebraic. The diffusion is enhanced and a superdiffusion is characteristic of the test particle motion for long times. It is shown that for long times [Formula Presented] is independent of the mass ratio [Formula Presented] The mass ratio is an important parameter controlling a transition time before which [Formula Presented] and after which diffusion is enhanced. Special attention is given to the Rayleigh limit where ε is small. It is shown that when [Formula Presented] our results are identical to those obtained within the framework of the Lévy walk model.