Numerical study of anomalous diffusion of light in semi-crystalline polymer structures

TL;DR

This paper numerically investigates anomalous light diffusion in semi-crystalline polymers, revealing how nonlocal interactions influence transport and localization, with potential applications across various scientific fields.

Contribution

It introduces a numerical approach to study anomalous diffusion in disordered systems using a fractional Laplacian spectrum, highlighting the effects of super- and sub-diffusion.

Findings

Enhanced transport observed for s<1 (super-diffusion)

Localization increases for s>1 (sub-diffusion)

Transport can be improved at specific scales even in sub-diffusive regimes

Abstract

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.