  A static electric field of a few V/cm shifts the energy levels of ultracold
Rydberg atoms in a magneto-optical trap. For a given principle quantum number,
most of the energy levels are nearly degenerate at zero field and fan out with
increasing field to form a manifold. We excite Rydberg atoms to energy levels
near the center of the manifold, where the spacing is nearly harmonic, and
allow them to exchange energy via resonant dipole-dipole interactions. We
measure the time evolution as energy spreads away from the center of the
manifold, which reveals that the system fails to thermalize for long
interaction times. A computational model that includes only a few essential
features of the system qualitatively agrees with this result.
