Quantum Particle on a Random Graph

For one of my research projects, I have been teaching myself about the topic of random graphs. I saw an opportunity to combine some of the interesting behaviors of random graphs, specifically that they undergo a percolation/connectivity phase transition, with the basic quantum physics of particles confined to lattices, which themselves undergo a conductor-insulator transition in the presence of a disordered mean field.

A disordered mean field in a networked “solid” leads to enhanced localization of a quantum particle, even in the presence of a giant network component.

I wrote about what I found in a semi-pedagogical post on Wolfram Community, which you can find here.

-Matt