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The density operator of the arbitrary physical system must be positivedefinite. Employing the general master equation technique which preserves thisproperty we derive equations of motion for the density operator of an activeatom which interacts collisionally with the reservoir of perturber atoms. Theobtained general relations applied to the two-level atom yield Bloch-Boltzmannequations (BBE). The form of the BBE obtained by us differs from that knownfrom literature which, as we show, are not guaranteed to preserve the requiredpositivity. We argue that our results are the correct ones and as such shouldbe used in practical applications. Moreover, the structure and the terms whichappear in our set of BBE seem to allow simpler and more straightforwardphysical interpretation.Comment: 23 pages, no figure

Completely positive Bloch-Boltzmann equations