A stochastic dilation of master equation for a maser is constructed using the technique of quantum stochastic differential equations with unbounded operator coefficients. The associated quantum Markov flow is characterized and turns out to extend a classical birth and death process. Furthermore, the stationary distribution of the aforementioned process, which is connected to the stationary state of the micromaser, is obtained in a closed form.
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Fagnola et al. (1994) studied this question.
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