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The Lindblad and Redfield forms derived from the Born–Markov master equation without secular approximation and their applications

Chang-Yao Liao,Xian-Ting Liang

Figure 1. The evolution of the reduced density matrix for a three-level quantum system obtained using the non-secular equations (Lindblad and Redfield forms) with

${{\rm{\Gamma }}}_{\alpha \beta }^{(2)}({\omega }_{{mn}})$ (a) and

${{\rm{\Gamma }}}_{\alpha \beta }^{(1)}({\omega }_{{mn}})$ (b); secular equations with

${{\rm{\Gamma }}}_{\alpha \beta }^{(2)}({\omega }_{{mn}})$ (c), and

${{\rm{\Gamma }}}_{\alpha \beta }^{(1)}({\omega }_{{mn}})$ (d). Here, we set the the environmental spectral density function to the Drude form, with η = 0.125, Ω = 100.0 cm⁻¹, T = 300 K. The initial state is set to ρ(0) = ∣1⟩⟨1∣. In equation (37), N = 100.