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We consider population transfer in open quantum systems, which are describedby quantum dynamical semigroups (QDS). Using second order perturbation theoryof the Lindblad equation, we show that it depends on a weak external field onlythrough the field's autocorrelation function (ACF), which is phase independent.Therefore, for leading order in perturbation, QDS cannot support dependence ofthe population transfer on the phase properties of weak fields. We examine anexample of weak-field phase-dependent population transfer, and show that thephase-dependence comes from the next order in the perturbation.

The Scaling of Weak Field Phase-Only Control in Markovian Dynamics