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The chain of kinetic equations for three-level macroscopic systems intersecting with an electromagnetic field on the basis of then method of elimination of the boson variables is obtained. On its basis the role of two-photon transitions is investigated.
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Eugene K. Bashkirov, "Kinetics equations for superradiance in three-level systems," Proc. SPIE 4589, Optical Fiber for Telecommunication in Russia, (24 October 2001); https://doi.org/10.1117/12.445689