  Unitary evolution in PT-symmetric quantum mechanics with a time-dependent
metric is found to yield a new class of adiabatic processes. As an explicit
example, a Berry-like phase associated with a PT-symmetric two-level system is
derived and interpreted as the flux of a fictitious monopole with a tunable
charge plus a singular string component with non-trivial phase contributions.
The Hermitian analog of our results is also discussed.
