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

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 exhib...

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Bibliographic Details
Published inarXiv.org
Main Authors Kalozoumis, P A, Pappas, G, Diakonos, F K, Schmelcher, P
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.08.2015
Subjects
Broken symmetry
Eigenvectors
Local current
Order parameters
Phase diagrams
Physics - Optics
Physics - Quantum Physics
Scattering
Symmetry
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1407.2655