Perturbative dynamics of open quantum systems by renormalization group method

We analyze perturbative dynamics of a composite system consisting of a quantum mechanical system and an environment by the renormalization group (RG) method. The solution obtained from the RG method has no secular terms and approximates the exact solution for a long time interval. Moreover, the RG method causes a reduction of the dynamics of the composite system under some assumptions. We show that this reduced dynamics is closely related to a quantum master equation for the quantum mechanical system. We compare this dynamics with the exact dynamics in an exactly solvable spin-boson model.

Figure 1

Plots of time evolution of the fidelity of the TCL, RWA, and RG solutions with the exact solution. The parameters are (a) $\mathrm{\Delta }=10{\lambda }^2$ and $\alpha =5{\lambda }^2$ and (b) $\mathrm{\Delta }=10{\lambda }^2$ and $\alpha ={\lambda }^2$.