We consider dissipation operators used in Quantum Optics for the description of quantum spontaneous emission in the context of damped driven Jaynes–Cummings equations. The equations describe quantized one-mode Maxwell field coupled to a two-level molecule. The nonpositivity of two basic dissipation operators is proved in the framework of the theory of the Hilbert space of the Hilbert–Schmidt operators. We show that one of the operators is symmetric, while the other is not.
Komech et al. (Sun,) studied this question.