Physics – Quantum Physics
Scientific paper
2007-06-16
Europhys. Lett. 82, 20007 (2008)
Physics
Quantum Physics
Scientific paper
10.1209/0295-5075/82/20007
Based 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.
Duzzioni E. I.
Moussa M. H. Y.
Serra Roberto M.
No associations
LandOfFree
A general treatment of geometric phases and dynamical invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A general treatment of geometric phases and dynamical invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A general treatment of geometric phases and dynamical invariants will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-332206