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

PT-symmetric Double Well Potentials Revisited: Bifurcations, Stability and Dynamics