Lecture notes on Quantum Diffusion and Random Matrix Theory

TL;DR

This paper introduces a novel approach combining quantum diffusion and random matrix theory to analyze the diffusive limit of the random Schrödinger equation, providing a simplified, self-contained presentation of recent joint work.

Contribution

It presents a new methodology linking quantum diffusion with random matrix theory to better understand the diffusive limit of the random Schrödinger equation.

Findings

Develops a new theoretical framework for quantum diffusion.

Simplifies complex ideas into accessible lecture notes.

Bridges concepts from random matrix theory and quantum physics.

Abstract

In joint work with Adam Black and Reuben Drogin, we develop a new approach to understanding the diffusive limit of the random Schrodinger equation based on ideas taken from random matrix theory. These lecture notes present the main ideas from this work in a self-contained and simplified presentation. The lectures were given at the summer school "PDE and Probability" at Sorbonne Universit\'e from June 16-20, 2025.