A general treatment of geometric phases and dynamical invariants

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dc.creatorDuzzioni, E. I.
dc.creatorSerra, R. M.
dc.creatorMoussa, M. H. Y.
dc.date2007-06-16
dc.date2008-02-28
dc.date.accessioned2026-07-07T09:32:47Z
dc.date.available2026-07-07T09:32:47Z
dc.descriptionBased only on the parallel transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee's non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non-Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature.
dc.identifierhttps://arxiv.org/abs/0706.2448
dc.identifierhttp://arxiv.org/abs/0706.2448
dc.identifierEurophys. Lett. 82, 20007 (2008)
dc.identifierdoi:10.1209/0295-5075/82/20007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158907
dc.subjectQuantum Physics
dc.titleA general treatment of geometric phases and dynamical invariants
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