Approach to Equilibrium in the Micromaser

We examine the approach to equilibrium of the micromaser. Analytic methods are first used to show that for large times (i.e. many atoms) the convergence is governed by the next to leading eigenvalue of the corresponding discrete evolution matrix. The model is then studied numerically. The numerical results confirm the phase structure expected from analytic approximation methods and agree for large times with the analysis of Elmfors et al in terms of the continuous master equation. For short times, however, we see evidence for interesting new structure not previously reported in the literature.