We study the sets of possible sign changes that can occur when $n$ real quantum states are transported adiabatically around an $n$-fold degeneracy. The allowed sign changes include those predicted by the familiar spin $j=(n-1\mathrm{})/2$ model as a subset, but we also find at least one other possible set of sign changes for each $n>\mathrm{}2\mathrm{}$. Experimentally verifiable quadrilateral billiard examples are presented to illustrate these additional possibilities for 3- and 4-fold degeneracies.

• Received 3 November 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.2223