B. Simon, "Holonomy, the quantum adiabatic theorem, and Berry's phase," Phys. Rev. Lett. 51, 2167--2170 (1983).  Home/Search   Document Not in Database   Summary   APS   Related Articles   Check

....Information Physics UniversityofTokyo, Bunkyo ku,Tokyo 113, Japan 1 1 Introduction Berry s phase, discovered by M. V,Berry in 1982, convienced by many experiments, is naturally interpreted as a curvature of natural connection introduced on the line bundle over the space of pure states [1] 2] 19][20]. Berry s phase is a manifestation of non commutative nature. Actulally, various quantum mechanical phenomina, such as quantum hall effect, Aharanov Bohm effect, Yang Tailor effect, and so on, cannot be predicted by naive analogy of classical mechanics, and are explained in terms of Berry s ....

B. Simon, "Holonomy, the quantum adiabatic theorem, and Berry's phase," Phys. Rev. Lett. 51, 2167--2170 (1983).

....density matrices. One is Uhlmann s parallelism and the other is Nagaoka s information geometry. Uhlmann s parallelism is generalization of Berry s phase, which, by far confirmed by several experiments, is a holonomy of a natural connection in the line bundle over the space of pure states [1] 3] 12][13]. In 1986, Uhlmann generalized the theory to include mixed states in the Hilbert space H [14] 15] 16] It is pointed out that the Uhlmann s parallelism is deeply concerned with quantum estimation theory. Concretely speaking, iff Uhlmann s curvature vanishes, SLD CR bound is attained, which ....

B. Simon, "Holonomy, the quantum adiabatic theorem, and Berry's phase," Phys. Rev. Lett. 51, 2167--2170 (1983).

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