Geometric phase in open systems.

We calculate the geometric phase associated with the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main sources of decoherence are considered: dephasing and spontaneous decay. We show that the geometric phase is completely insensitive to the former, i.e., it is independent of the number of jumps determined by the dephasing operator