We establish a formula for the probability of a quantum adiabatic transition between two permanently degenerate energy levels which do not cross. This formula corresponds to the non-Abelian generalization of the Landau-Dykhne formula that is valid for the nondegenerate case. It applies in particular in cases of symmetry-induced degeneracy, a typical example being the Kramer degeneracy.
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Joye et al. (1993) studied this question.
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