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arXiv · 1910.02298

Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay

Ludmila Praxmeyer·Konstantin G. Zloshchastiev
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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.

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Ludmila Praxmeyer, Konstantin G. Zloshchastiev. 2019-10-05. Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay. https://doi.org/10.1142/s0217979218502764

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