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Letters in Mathematical Physics

, Volume 106, Issue 12, pp 1817–1835 | Cite as

Non-Real Eigenvalues for \({{\mathcal{PT}}}\)-Symmetric Double Wells

  • Amina Benbernou
  • Naima Boussekkine
  • Nawal Mecherout
  • Thierry Ramond
  • Johannes SjöstrandEmail author
Article

Abstract

We study small, \({{\mathcal{PT}}}\)-symmetric perturbations of self-adjoint double-well Schrödinger operators in dimension \({n\ge 1}\). We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the perturbation gets stronger.

Keywords

PT-symmetry Schrödinger operator double well eigenvalues 

Mathematics Subject Classification

35P20 35Q40 81Q12 81Q20 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Amina Benbernou
    • 1
  • Naima Boussekkine
    • 1
  • Nawal Mecherout
    • 1
  • Thierry Ramond
    • 2
  • Johannes Sjöstrand
    • 3
    Email author
  1. 1.Faculté des Sciences Exactes et InformatiqueUniversité de MostaganemMostaganemAlgeria
  2. 2.Laboratoire de Mathématiques d’OrsayUniversité Paris-Sud, CNRS, Université Paris-SaclayOrsayFrance
  3. 3.Institut de Mathématiques de Bourgogne (UMR 5584 du CNRS)Université de BourgogneDijon CedexFrance

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