Levy walks and generalized stochastic collision models

A stochastic collision model is studied in which a test particle of a mass M collides with bath particles of another mass m. 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 < x(2)(t)> is independent of the mass ratio epsilon= m/M. The mass ratio is an important parameter controlling a transition time before which < x(2) >similar to t and after which diffusion is enhanced. Special attention is given to the Rayleigh limit where epsilon is small. It is shown that when epsilon=1 OUT results are identical to those obtained within the framework of the Levy walk model.