  In this work we analyze PT-symmetric double-well potentials based on a
two-mode picture. We reduce the problem into a PT-symmetric dimer and
illustrate that the latter has effectively two fundamental bifurcations, a
pitchfork (symmetry-breaking bifurcation) and a saddle-center one, which is the
nonlinear analog of the PT-phase-transition. It is shown that the symmetry
breaking leads to ghost states (amounting to growth or decay); although these
states are not true solutions of the original continuum problem, the system's
dynamics closely follows them, at least in its metastable evolution. Past the
second bifurcation, there are no longer states of the original continuum
system. Nevertheless, the solutions can be analytically continued to yield a
new pair of branches, which is also identified and dynamically examined. Our
explicit analytical results for the dimer are directly compared to the full
continuum problem, yielding a good agreement.
