Anomalous ballistic diffusion

We introduce a novel two-component random network. Unit resistors are placed at random along the bonds of a pure superconducting linear chain, with the distance l between successive resistors being chosen from the distribution P(l)l-(+1) where >0 is a tunable parameter. We study the transport exponents dw and defined by x2t2dw and L, where x2 is the mean-square displacement, the resistivity, and L the system size. We find that for 1 both dw and stick at their value for a nonzero concentration of resistors. For <1 they vary continuously with: dw=2 and =. In the presence of a bias field, we find dw=. This is the first exactly soluble model displaying "anomalous ballistic diffusion," which we interpret physically in terms of a Lévy-flight-type random walk on a linear chain lattice.