Systematic pathway to PT-symmetry breaking in scattering systems (vol 90, 043809, 2014)

Recently [Phys. Rev. Lett. 106, 093902 (2011)] it has been shown that PT -symmetric scattering systems with balanced gain and loss undergo a transition from PT -symmetric scattering eigenstates, which are norm preserving, to symmetry broken pairs of eigenstates exhibiting net amplification and loss. In the present work we derive the existence of an invariant nonlocal current which can be directly associated with the observed transition playing the role of an "order parameter." The use of this current for the description of the PT -symmetry breaking allows the extension of the known phase diagram to higher dimensions incorporating scattering states which are not eigenstates of the scattering matrix.