On Kinetic Theory of Energy Losses in Randomly Heterogeneous Medium

TL;DR

This paper develops a kinetic theory describing how particles lose energy in fractal media with heterogeneities, revealing a sublinear power-law relationship between energy loss and distance.

Contribution

It derives a new equation for the distribution of energy losses in fractal media with quenched and dynamic heterogeneities, highlighting anomalous sublinear dependence.

Findings

Energy losses follow a power-law with exponent D-2.

In fractal dimension 2<D<3, losses scale as x^{D-2}.

The derived equation captures the distribution of energy losses in complex media.

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