Coarse-grained master equation is valid for a fast bath and any drive

We compare three master equations: Davies-Lindblad, Redfield, and the recent Coarse-grained competely positive equation[1]. We note that the Redfield equation is valid for a fast bath regardless of the relative strength of the coupling to the system Hamiltonian. The main obstruction to using it is its non-positivity. We show how an attempt to make Redfield positive results in the Coarse-grained master equation. Our new derivation allows to estimate the error of the resulting completely positive equation. Much like Redfield, this equation is applicable for fast bath even if the system Hamiltonian is driven. We thus present a completely positive open system master equation that is a controlled approximation to true evolution for any time-dependence of the system Hamiltonian. The fast bath assumption includes any bath with time correlation function decaying faster than 1/t² which is the case for the Ohmic bath. For Ohmic bath, equation is still applicable up to a large timescale.

[1] C. Majenz, T. Albash, H.-P. Breuer, and D. A. Lidar, Phys. Rev. A 88, 012103 (2013)