Exact solution and scaling theory of superradiance

The general scaling theory of transient phenomena near the instability point, which has been proposed by one of the present authors (M.S.), is applied to investigate the fluctuation and relaxation of superradiance near the complete inversion (or instability point). An exact solution for a simple model of superradiance has been obtained to study the relaxation and fluctuation of it near the complete inversion and to confirm the validity of the scaling theory. It is found that this asymptotic evaluation method yields very good results for a large system size Ω. The Ω-expansion method by van Kampen and by Kubo et al. is also discussed in this model in order to clarify the connection of it with the scaling theory.