  We argue that the quenched ultracold plasma presents an experimental platform
for studying quantum many-body physics of disordered systems in the long-time
and finite energy-density limits. We consider an experiment that quenches a
plasma of nitric oxide to an ultracold system of Rydberg molecules, ions and
electrons that exhibits a long-lived state of arrested relaxation. The
qualitative features of this state fail to conform with classical models. Here,
we develop a microscopic quantum description for the arrested phase based on an
effective many-body spin Hamiltonian that includes both dipole-dipole and van
der Waals interactions. This effective model appears to offer a way to envision
the essential quantum disordered non-equilibrium physics of this system.
