  From the spread of pollutants in the atmosphere to the transmission of
nutrients across cell membranes, anomalous diffusion processes are ubiquitous
in natural systems. The ability to understand and control the mechanisms
guiding such processes across various scales has important application to
research in materials science, finance, medicine, and energetics. Here we
present a numerical study of anomalous diffusion of light through a
semi-crystalline polymer structure where transport is guided by random disorder
and nonlocal interactions. The numerical technique examines diffusion
properties in one-dimensional (1D) space via the spectrum of an Anderson-type
Hamiltonian with a discrete fractional Laplacian operator (-{\Delta})^s, 0<s<2
and a random distribution of disorder. The results show enhanced transport for
s<1 (super-diffusion) and enhanced localization for s>1 (sub-diffusion) for
most examined cases. An important finding of the present study is that
transport can be enhanced at key spatial scales in the sub-diffusive case,
where all states are normally expected to be localized for a (1D) disordered
system.
