Nonlinear quantum effects in the maser model: a large N scaling behaviour

The time evolution of the mean photon number is numerically studied for different initial conditions. We find an approximate scaling of the curves for the various values of N when they are plotted against τ = t/Nα and the coefficient α, empirically determined, is found to be directly related to the spectral distribution of the initial condition over the exact states. Its value can be obtained from the N-dependence of the relevant eigenvalues. The approximate periodicity of the curves can also be understood in terms of the spectral distribution of the initial condition. (author)