Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay
arXiv:1910.02298 · doi:10.1142/S0217979218502764
Abstract
The 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.
arXiv comment8 pages, 3 composite figures, final/published version
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