Geometric phases and multiple degeneracies in harmonic resonators

In a recent experiment Lauber et al. have deformed cyclically a microwave r esonator and have measured the adiabatic normal-mode wave functions for eac h shape along the path of deformation. The nontrivial observed cyclic phase s around a threefold degeneracy were accounted for by Manolopoulos and Chil d within an approximate theory. However, open-path geometrical phases disag ree with experiment. By solving exactly the problem, we find unsuspected ex tra degeneracies around the multiple one that account for the measured phas e changes throughout the path. It turns out that proliferation of additiona l degeneracies around a multiple one is a common feature of quantum mechani cs.