Integrable models are uniquely simple physical systems with a sufficient number of conserved quantities to trivialize their dynamics. This means that they are exactly solvable, a rare thing even in classical mechanics. They also hide in quantum field theories where their solvability can uplift to give us important toy models, which allow us to ask questions that would be difficult to approach otherwise.
We obtained this model as the high energy limit of adjoint QCD in two dimensions. When the dynamics are solved for in the Mathematica file above, it is clear that the system is integrable as the initial and final sets of momenta are the same. Notice that the particles have identity (colors above), but that asympotically they have a preferred ordering. Both the line and circle geometries are available in the above code. Enjoy playing around!
