Non-Abelian geometric effect in quantum adiabatic transitions

Alain Joye (1) , Charles-Edouard Pfister (2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 EPFL - Ecole Polytechnique Fédérale de Lausanne

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.

Domaines: Physique mathématique [math-ph]

Alain Joye, Charles-Edouard Pfister. Non-Abelian geometric effect in quantum adiabatic transitions. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 1993, 48 (4), ⟨10.1103/PhysRevA.48.2598⟩. ⟨hal-01221147⟩