Geometric phase for mixed states: a differential geometric approach

  • S. Chaturvedi
  • E. Ercolessi
  • G. Marmo
  • G. Morandi
  • N. Mukunda
  • R. Simon
theoretical physics


A new definition and interpretation of the geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected principal fiber bundles, and the well-known Kostant-Kirillov-Souriau symplectic structure on (co-) adjoint orbits associated with Lie groups. It is shown that this framework generalizes in a natural and simple manner to the mixed state case. For simplicity, only the case of rank two mixed state density matrices is considered in detail. The extensions of the ideas of null phase curves and Pancharatnam lifts from pure to mixed states are also presented.


Mixed State Pure State Density Matrice Fiber Bundle State Case 
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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  • S. Chaturvedi
    • 1
  • E. Ercolessi
    • 2
  • G. Marmo
    • 3
  • G. Morandi
    • 4
  • N. Mukunda
    • 5
  • R. Simon
    • 6
  1. 1.Department of PhysicsUniversity of HyderabadHyderabadIndia
  2. 2.Dipartimento di FisicaUniversita di Bologna, INFM and INFNBolognaItaly
  3. 3.Dipartimento di Scienze FisicheUniversita di Napoli Federico II and INFNNapoliItaly
  4. 4.Dipartimento di FisicaUniversita di Bologna, INFM and INFNBolognaItaly
  5. 5.Centre for Theoretical StudiesIndian Institute of ScienceBangaloreIndia
  6. 6.The Institute of Mathematical SciencesTharamaniIndia

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