Resonant processes in a frozen gas

We present a theory of resonant processes in a frozen gas of atoms interacting via dipole-dipole potentials that vary as r(-3), when r is the interatomic separation. We supply an exact result for a single atom in a given state interacting resonantly with a random gas of atoms: in a different state. The time development of the transition process is calculated both on and off resonance, and the linewidth with respest to detuning is obtained as a function of time t. We introduce a random spin Hamiltonian to model a dense system of resonators, and show how it reduces to the previous model in the limit of a sparse system. We derive approximate equations for the average effective spin, and we use them to model the behavior seen in the experiments of Anderson, Veale, and Gallagher and Low ell and co-workers . The approach to equilibrium is round to be proportional to exp(-root gamma(eq)t), where the constant gamma(eq) is explicitly related to the: system's parameters. [S1050-2947(99)10505-5].