Why does the Redfield equation model thermal relaxation while the Lindblad equation does not?

Question

In open quantum systems, we model a process known as thermal relaxation. What is this process, and why is it that only the Redfield equation models this process, and the Lindblad equation doesn't?

Answer 1

In open quantum systems, the evolution of the total System is unitary. The freedom degrees of the environment is large, so we always think the environment will not evolve and that is the Born approximation.$$\rho(t) = \rho_{s}(t)\otimes\rho_{E}$$ The relaxation time means the time what the environment need back to equilibrium again. Redfield equation is always the Non-Markovian master equation, so we have to consider the relaxation time, the Lindblad equation is always Markovian, so we don't consider the relaxation time here.