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Non-Abelian generalization of off-diagonal geometric phases

David Kult·Johan Åberg·Erik Sjöqvist
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Abstract

If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.

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David Kult, Johan Åberg, Erik Sjöqvist. 2006-12-19. Non-Abelian generalization of off-diagonal geometric phases. https://doi.org/10.1209/0295-5075/78/60004

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