Statistical approach to fractal-structured systems: An illustration from the physics of semiconductor heterostructures

Physico-chemical systems presenting fractal-like structures pose difficulties for their study within the scope of the standard statistical mechanics. A way around in order to make predictions for analyzing the system properties consists into resorting to auxiliary alternative statistics. We illustrate here one such a case in a study of luminescence spectra in nanometric quantum wells of semiconductor heterostructures which show anomalous behavior when compared with the usual one in bulk matter. This is a result of the occurrence of the phenomenon in constrained geometries (nanometer scales) with microroughened fractal-like boundaries. This sets practical difficulties for the theoretical treatment in that one does not have access to a proper description of certain relevant characteristics of the system. The situation becomes further hard to deal with when the system is in far-from-equilibrium conditions. A way around to perform a study of the phenomenon consists into the use of a formalism for dealing with nonequilibrium many-body systems based on auxiliary statistics, and we resort here to Renyi approach adapted to a nonequilibrium statistical ensemble formalism.