Non-Abelian geometric effect in quantum adiabatic transitions

Abstract : 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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Alain Joye, Charles-Edouard Pfister. Non-Abelian geometric effect in quantum adiabatic transitions. Physical Review A, American Physical Society, 1993, 48 (4), ⟨10.1103/PhysRevA.48.2598⟩. ⟨hal-01221147⟩

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