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

TL;DR

This paper develops a phase space approach to non-Hermitian quantum systems, revealing how environmental interactions influence decay rates and can stabilize certain states, challenging traditional decay assumptions.

Contribution

It introduces a phase space formulation of density operators for non-Hermitian Hamiltonians, linking decay properties to energy eigenvalues and resonance conditions.

Findings

Mean lifetime depends on energy eigenvalues in non-Hermitian systems.

Resonance conditions can lead to long-lived, stable quantum states.

Dissipative effects may support stability rather than cause decay.

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.