Out of thermal equilibrium state, the vacuum is unstable and evolves in time. Consequently, the annihilation operators associated with the unstable vacuum depend on time. This dissipative time-evolution of quantum systems can be systematically treated, within the canonical operator formalism referred to as non-equilibrium thermo-field dynamics. Given is an alternative route to derive the time-dependent annihilation operators within the formalism. As an example, time-dependent annihilation operators for the systems of bosonic and fermionic semi-free fields are derived.

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