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 4. The evolution of the reduced density matrix for the PE545 model obtained using the non-secular and secular equations (Lindblad and Redfield forms) with ${{\rm{\Gamma }}}_{\alpha \beta }^{(2)}({\omega }_{{mn}})$ and ${{\rm{\Gamma }}}_{\alpha \beta }^{(1)}({\omega }_{{mn}})$, where the meanings of (a)-(d) are similar to those of figure 1. We set the the environmental spectral density function to the Drude form, with η = 12.5, Ω = 1000.0 cm−1, and T = 300 K. The initial state is set to ρ(0) = ∣1⟩⟨1∣. In equation (37), N = 10000.