Abstract
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-eld 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 elds are derived.
Highlights
IntroductionOne of the basic frameworks used in treating dissipative quantum systems is given by the quantum Liouville equation (the quantum master equation)
One of the basic frameworks used in treating dissipative quantum systems is given by the quantum Liouville equation ∂ ∂t ρ(t) = −iLρ(t), (1)with the properties of the Liouville operator L,† = iL, (2) tr L = 0, (3)and the condition of ρ(t) at the initial time t = 0: ρ†(0) = ρ(0)
NETFD provides us with a canonical operator formalism for dissipative quantum systems which preserves most of the technical properties in usual quantum field theory (QFT)
Summary
One of the basic frameworks used in treating dissipative quantum systems is given by the quantum Liouville equation (the quantum master equation). Note that the vacuum |0(t) within NETFD is unstable and dependent on time, the situation being quite different from the case in usual quantum field theory (QFT). NETFD provides us with a canonical operator formalism for dissipative quantum systems which preserves most of the technical properties in usual QFT. We show an alternative route to derive the annihilation operators γt and γt They were derived in relation to the time-dependent annihilation operators γ(t) and γ(t) for unstable physical particles which annihilate the initial vacuum |0 = |0(t = 0) , i.e., γ(t)|0 = 0 and γ(t)|0 = 0 [5,6,7,9] (see appendix A). The conventional derivation of the annihilation operators is given in appendix A
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