Anomalous transport in a one-dimensional Lorentz gas model.

Employing the generalized master equation proposed in [R. Friedrich et al., Phys. Rev. Lett. 96, 230601 (2006)], we derive a kinetic equation for a random kick model. For a particular choice of the time evolution kernel, a fractional master equation is obtained, which can be related to a Levy walk. In one dimension, we use this model to describe a stochastic Lorentz gas with an annealed disorder. Exact moment relations are obtained in Laplace space, and the long-time behavior of the moments is discussed. The results are compared to those of related models.