Nonclassical Impurity Transport in the Dykhne Model with Coordinate-Dependent Parameters. Fermat Principle

An asymptotic theory of impurity transport has been developed for the simplest regularly inhomogeneous medium (Dykhne model, demonstrating subdiffusive transport regime) with parameters obeying large-scale spatial dependences. The results for concentration at distances from impurity source greatly exceeding the size of main impurity localization region are expressed in terms of linear integrals along concentration-signal trajectories. The latter are obtained from the variational principle, which is an analogue of the Fermat principle in geometric optics. Integrals along trajectories are analogues of optical path length. The form of these integrals depends on transport regime, and the trajectories may be either 2D and 3D curves (depending on the regime).