Anomalous energy losses in fractal medium

Abstract

We derive equation describing distribution of energy losses of the particle propagating in fractal medium with quenched and dynamic heterogeneities. We show that in the case of the medium with fractal dimension $2<D<3$ the losses of energy are described by the Mittag-Leffler renewal process. The average energy loss of the particle experiences anomalous drift $\Delta\sim x^{\alpha}$ with power-law dependence on the distance $x$ from the surface and exponent $\alpha=D-2$.