∮ A·dl

That's a contour integral — you add something up all the way around a closed loop and come back to where you started. For three years it was most of my life.

Send an electron around a loop with a magnetic field sealed inside, where the electron never goes. Classically nothing should happen: no field where the particle is, no force, no effect. It happens anyway. The electron picks up a phase shift proportional to that integral, and you can see it in the interference pattern.

The field is zero everywhere the electron travels. It still knows the solenoid is there. That's the Aharonov–Bohm effect, and I spent those years trying to simulate the molecular version of it faster than anyone had managed.

I left before writing up the thesis. The physics is still lovely. The readable version is here (PDF).