Environmentally induced corrections to the geometric phase in a two-level system

We calculate the geometric phase for different open systems (spin-boson and spin-spin models). We study not only how they are corrected by the presence of the different type of environments but also discuss the appearence of decoherence effects. These should be taken into account when planning experimental setups to study the geometric phase in the nonunitary regime. We propose a model with slow decoherence rate in which the geometric phase is still modified and might be measured.