Fokker-Planck equation for transport of wave packets in nonlinear disordered media

TL;DR

This paper develops a Fokker-Planck equation-based theory to describe wave packet transport in nonlinear disordered media, extending previous results and providing a unified framework for understanding such complex systems.

Contribution

It introduces a novel derivation of a Fokker-Planck transport equation for wave packets in nonlinear disordered media of any dimension, based on a diagrammatic expansion.

Findings

Confirms previous results in 2D nonlinear disordered media

Provides a heuristic Boltzmann equation interpretation

Establishes a general framework for wave packet transport

Abstract

Starting from first principles, we formulate a theory of wave packet propagation in a nonlinear, disordered medium of any dimension, through the derivation of a Fokker-Planck transport equation. Our theory is based on a diagrammatic expansion of the wave packet's density, and is supported by a heuristic picture that involves a Boltzmann equation with an effective, external potential. Our approach also confirms results obtained in previous work for two-dimensional, nonlinear disordered media.