Applications of the complex geometric phase for metastable systems.

Garrison and Wright showed that upon undergoing cyclic quantum evolution a meta-stable state acquires both a geometric phase and a geometric decay probability. This is described by a complex geometric “phase” associated with the cyclic evolution of two states and is closely related to the two state formalism developed by Aharonov et al.. Applications of the complex geometric phase to the Born–Oppenheimer approximation, the Aharonov–Bohm effect, the propagation of light through absorbing birefringent crystals and Hannay’s angle are considered.