Feynman graphs and renormalization in quantum diffusion

TL;DR

This paper reviews how, in a scaling limit, the evolution of a quantum particle in a static random environment results in diffusion, emphasizing the roles of Feynman graphs and renormalization techniques.

Contribution

It provides a proof connecting quantum diffusion in random environments to classical diffusion equations, highlighting the use of Feynman graphs and renormalization methods.

Findings

Quantum particle evolution converges to diffusion in the scaling limit

Feynman graph expansions are crucial for the proof

Renormalization techniques facilitate the analysis

Abstract

We review our proof that in a scaling limit, the time evolution of a quantum particle in a static random environment leads to a diffusion equation. In particular, we discuss the role of Feynman graph expansions and of renormalization.