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arXiv · 1407.2655

Systematic pathway to ${\mathcal{PT}}$ symmetry breaking in scattering systems

P. A. Kalozoumis·G. Pappas·F. K. Diakonos·P. Schmelcher
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Abstract

Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from $\mathcal{PT}$-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 non-local 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 $\mathcal{PT}$-symmetry breaking allows the extension of the known phase diagram to higher dimensions incorporating scattering states which are not eigenstates of the scattering matrix.

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P. A. Kalozoumis, G. Pappas, F. K. Diakonos, P. Schmelcher. 2015-08-25. Systematic pathway to ${\mathcal{PT}}$ symmetry breaking in scattering systems. https://doi.org/10.1103/physreva.90.043809

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