  Anholonomies in eigenstates are studied through time-dependent variations of
a magnetic flux in an Aharonov-Bohm ring. The anholonomies in the eigenenergy
and the expectation values of eigenstates are shown to persist beyond the
adiabatic regime. The choice of the gauge of the magnetic flux is shown to be
crucial to clarify the relationship of these anholonomies to the eigenspace
anholonomy, which is described by a non-Abelian connection in the adiabatic
limit.
