General Setting for Geometric Phase of Mixed States in Open Systems - Ali Rezakhani

In this talk, the problem of a geometric phase for an open quantum system is described in a unifying approach. Two of the existing methods to define geometric phase, one by Uhlmann's approach and the other by a kinematic approach, which have been considered to be distinct, are shown to be related in this framework. The method is based on purification of a density matrix by its uniform decomposition, and hence, a generalization of the parallel transport condition. It is also shown how to recover the earlier known definitions of geometric phase as well as how to generalize them when degeneracy exists and varies in time.