An age-dependent model of cavity radiation and its detection

Cavity radiation is modelled as a population point process with age-dependent birth rate. A method of phases is introduced to analyze special types of age dependencies. The conditional life-time of the cavity photon is assumed to be in hypothetical phases, the life-span of the phases being distributed independently and exponentially. The analysis leads to an explicit differential equation for the generating function of the population size. The detection process is analyzed and an explicit expression for the correlation of the counts provided. By an appropriate choice of the parameters, the spectrum corresponding to Gaussian Lorentzian light is recovered. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.