Pt-symmetric Double-well Potentials Revisited: Bifurcations, Stability and Dynamics

This work presents a two-mode analysis of PT-symmetric double-well potentials. The problem is reduced to a PT-symmetric dimer and it is shown that there are effectively two fundamental bifurcations, a pitchfork bifurcation (symmetrybreaking bifurcation) and a saddle-center bifurcation (nonlinear analog of the PT-phase transition). It is shown that symmetry breaking leads to ghost states, which are associated with growth or decay; although these states are not true solutions of the original continuum problem, the dynamics of the system 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 are identified and examined. The explicit analytical results for the dimer are compared directly with the full continuum problem and good agreement is found.