Multiple-Time-Scale Analysis of Spontaneous Radiation Processes. II. Many-Particle Systems

The multiple-time-scale expansion method has been used to study a system of $N$ -two-level atoms with one of them excited initially. It is found that, in the limit of large time, the Schrödinger equation for the system reduces to a set of algebraic equations, and can thus be solved exactly. A detailed study of a four-atom system is given. The analysis is then extended to a regular lattice of $N$ atoms. It is found that in a large lattice, the probability for the excitation energy to be trapped is very large, even when the lattice spacing is comparable to the characteristic wavelength of the radiation.