The density operator of the arbitrary physical system must be positive definite. Employing the general master equation technique which preserves this property, we derive equations of motion for the density operator of an active atom which interacts collisionally with the reservoir of perturber atoms. The obtained general relations applied to the two-level atom yield Bloch-Boltzmann equations (BBE) which, as it is the case with master equation approach, are linear in the matrix elements of the active-atom density operator. The obtained BBE guarantee that positivity is preserved, which needs not to be the case with the results known from literature. We argue that our results are the correct ones and as such should be used in practical applications. Moreover, the structure and the terms which appear in our set of BBE seem to allow simpler and more straightforward physical interpretation.

• Received 30 January 2002

DOI:https://doi.org/10.1103/PhysRevA.68.013809