Correlated random walk in continuous space

We present a model for diffusion with correlated motion in continuous space. Correlation is implied as the retention of the directional memory of the moving particle between successive scattering events. We use a model borrowed from the field of polymers, based on a scattering angle theta, which is analogous to the bond angle between two monomers in a chain molecule. We monitor via Monte Carlo computer simulations the usual random walk properties, such as the mean-square displacement, the number of sites visited (where the underlying continous space is binned in boxes), etc., for two-dimensional spaces, as a function of time, and the correlation parameter. This type of motion belongs asymptotically to the same class as the regular random walk. For short times one observes a crossover that is strongly dependent on the correlation parameter in a scaling form, which is calculated numerically.