Scattering lengths and universality in superdiffusive L\'evy materials

We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the a…