Fresh news from Flatland: Testing scale invariance in the lab
A fluid is said to be scale-invariant when its interaction and kinetic energies have the same scaling in a dilatation operation. This symmetry, in association with the more general conformal invariance, has profound consequences on the equilibrium properties of the fluid as well as its dynamics.
In this talk, I will present recent experimental investigations of this phenomenon using an initially uniform, two-dimensional gas of rubidium atoms that is suddenly immersed in a harmonic potential. I will show an unexpected result for this setup: There exist specific initial shapes that lead to a periodic evolution of the system, corresponding to "breathers" of the two-dimensional Gross-Pitaevskii equation. I will conclude with a possible generalization of such phenomena to other scale invariant fluids.