Emergence of the Macroscopic Fourier Law from the Microscopic Wave Equation of Diffusive Medium

TL;DR

This paper derives the macroscopic Fourier law and diffusion equation from the microscopic Schrödinger equation in a diffusive medium, supported by numerical simulations, and generalizes the approach to other random wave equations.

Contribution

It presents a novel derivation of the Fourier law from the Schrödinger equation for diffusive media, bridging microscopic wave dynamics and macroscopic diffusion.

Findings

Successful derivation of Fourier law from Schrödinger equation

Numerical simulations support the theoretical model

Generalization to other random wave equations demonstrated

Abstract

The Fourier law and the diffusion equation are derived from the Schrodinger equation of a diffusive medium (consisting of a random potential). The theoretical model is backed by numerical simulation. This derivation can easily be generalized to demonstrate the transition from any random wave equation to the diffusive equation.