Praxmeyer, LudmilaZloshchastiev, Konstantin G.2025-12-232025-12-232018-10-10Praxmeyer, L. and Zloshchastiev, K.G. 2018. Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay. International Journal of Modern Physics B. 32(25): 1-8. doi:10.1142/S02179792185027640217-97921793-6578 (Online)isidoc: GW3QLhttps://hdl.handle.net/10321/6318The Wigner–Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean lifetime and decay constants of quantum systems do not necessarily take arbitrary values, but could become functions of energy eigenvalues and have a discrete spectrum. It is demonstrated also that a constraint upon mean lifetime and energy appears, which is used to derive the resonance conditions at which long-lived states occur. The latter indicate that quantum dissipative effects do not always lead to decay but, under certain conditions, can support stability of a system.8 penAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Non-Hermitian HamiltonianOpen systemDecay constantPhase spaceDensity operatorArticle2025-02-2710.1142/S0217979218502764