Geometric phase in open systems We need a description of geometric phase for mixed tate There have been various proposals for example via state purification (A. UhImann, Lett. Math. Phys. 21, 229(1991) through an interferometric procedure: E. Sjoqvist et al PRL 200 -or by pertur ative expansion (Gamliel, D. and Freed, J H. PRA 39, 3238(1989) R. Whitney, and Y. Gefen, Phys. Rev. Lett. 90, 190402)14 Geometric phase in open systems • We need a description of geometric phase for mixed state! There have been various proposals, for example: • -via state purification: (A. Uhlmann, Lett. Math. Phys. 21,229 (1991)) • -through an interferometric procedure: (E. Sjoqvist et al. PRL 2000), • -or by perturbative expansion: (Gamliel, D. and Freed, J. H. PRA 39, 3238(1989); R. Whitney, and Y. Gefen, Phys. Rev. Lett. 90, 190402 )