On kinetic theory of energy losses in randomly heterogeneous medium

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 $\Delta$ are characterized by the sublinear anomalous dependence $\Delta\sim x^{\alpha}$ with power-law dependence on the distance $x$ from the surface and exponent $\alpha=D-2$.