Geometry of 2-Fold Degenerated 2-Level System

  • M. V. Pletyukhov
  • E. A. Tolkachev
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 543)


It is well-known [1] that during the cyclic adiabatic evolution multi-level (quantum) system acquires the geometric phase factor, or Berry’s phase. B.Simon has shown [2] that it is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem naturally defines a connection in such a bundle. In the case of degenerated systems this factor is non-Abelian [3].


  1. 1.
    Berry, M.V.: Proc. R. Soc. A 392 (1984) 45.zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Simon, B.: Phys. Rev. Lett. 51 (1983) 2167.CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Wilchek, F., Zee, A.: Phys. Rev. Lett. 52 (1984) 2111.CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Pletyukhov, M., Tolkachev, E.: J. Phys.A 32(1999) 1073.zbMATHCrossRefMathSciNetADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • M. V. Pletyukhov
    • 1
  • E. A. Tolkachev
    • 1
  1. 1.Institute of Physics National Academy of Sciences of BelarusMinskBelarus

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