Violation of the mean path length invariance property.

The invariance property of the mean path length is an astonishing law of Nature governing the motion of particles inside a disordered material. Whatever the strength of the disorder, the property states that the mean path length is exclusively determined by the ratio between the volume and the surface. Till now, the property has been reported as universal and valid in any kind of disordered medium and also beyond diffusion conditions. Nevertheless, we found out that the property fails in anomalous transport and in other kinds of random walk. By means of Monte Carlo simulations of light transport, we show that, in these cases, the invariance property loses its validity and the mean path length becomes dependent on the diffusive characteristics of the medium. The critical issue of such a violation lies in the breaking of isotropy and homogeneity of the radiance in the whole volume. These results are valid for all natural or artificial phenomena where random walkers, whatever their nature, are able to experiment anomalous transport.