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Geometric phases of real wave functions in nonintegrable quantum billiards are measured using microwave resonators. They appear as a sign change of the wave function after a cyclic excursion around a diabolic point in the space of shapes of the resonator. For a path encircling a pointlike triple degeneracy of an integrable system, an unexpected sign change for two out of the three wave functions is found, which must be attributed to a hidden symmetry, and not to a Berry phase.
Lauber et al. (Mon,) studied this question.