Comments on some recent solutions of the superradiant master equation

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Abstract
The results of Haake and Glauber concerning the solution of the superradiant master equation of Bonifacio et al., are compared with those of Degiorgio and Ghielmetti. This is accomplished by using the atomic coherent-state representation of Arecchi et al., which provides a convenient mathematical formalism for the comparison. The relationship of these results to the recently presented exact Fokker-Planck-equation representation of Narducci, Coulter, and Bowden is discussed. This representation is used to prove the equivalence of the main conclusions derived by Degiorgio and Ghielmetti to a special case of the results of Haake and Glauber. In addition, it is shown that the expectation values calculated by Haake and Glauber are particular solutions of a coupled hierarchy of equations of motion constructed from the exact Fokker-Planck equation, neglecting the noise and diffusion terms.

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