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 distribu tion of time intervals between the collisions is long tailed, the rela xation 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 i ndependent of the mass ratio epsilon= m/M. The mass ratio is an import ant parameter controlling a transition time before which < x(2) >simil ar to t and after which diffusion is enhanced. Special attention is gi ven to the Rayleigh limit where epsilon is small. It is shown that whe n epsilon=1 OUT results are identical to those obtained within the fra mework of the Levy walk model.