Emergence of the Macroscopic Fourier Law from the Microscopic Wave   Equation of Diffusive Medium
  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. 
Er'el Granot, Nisim Cohen and Shmuel Sternklar