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Abstract:
After giving a heuristic derivation of the master equation that is commonly employed for modeling the dynamics of a damped harmonic oscillator, we focus on the algebraic properties of this master equation. In particular, we report the eigenvalues of its Liouville operator and the corresponding right and left eigenvectors. These tools are then used for a study of micromaser dynamics, where the harmonic oscillator is a privileged cavity mode of the radiation field. In addition to being damped, the mode is also driven by atoms that traverse the cavity one by one and interact strongly with the quantized radiation. The most important statistical properties of the exiting atoms are derived. For the sake of pedagogy, the treatment advances from the simple to the complicated, and the reader may benefit from numerous homework assignments.
