Are Directed Waves Multifractal?

TL;DR

This paper investigates the statistical properties of directed wave propagation in anisotropic media, deriving a Fokker-Planck equation, and concludes that such waves are not multifractal but fill space uniformly.

Contribution

It introduces a novel approach by mapping the Fokker-Planck equation to an su(1,1) ferromagnet and analyzes the wave function distributions.

Findings

Directed waves fill space uniformly

Directed waves do not exhibit multifractality

Symmetries help compute asymptotic distributions

Abstract

Wave propagation is studied in a sufficiently anisotropic random medium that backscattering along one direction can be neglected. A Fokker-Planck equation is derived the solution to which would provide a complete statistical description of such directed waves. The Fokker-Planck equation is mapped onto an su(1,1) ferromagnet and its symmetries are identified. Using the symmetries asymptotic wave function distributions are computed and used to show that directed wave functions fill space uniformly and do not have multifractal character.