Geometric phase for mixed states: a differential geometric approach

Details Geometric phase for mixed states: a differential geometric approach Geometric phase for mixed states: a differential geometric approach

2003-12-17

arxiv.org/abs/quant-ph/0312146v1

Physics

Quantum Physics

22 pages, revtex4

Scientific paper

10.1140/epjc/s2004-01814-5

A new definition and interpretation of 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 Fibre Bundles, and the well known Kostant-Kirillov-Souriau symplectic structure on (co) adjoint orbits associated with Lie groups. It is shown that this framework generalises 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.

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