PT-symmetry and Schrodinger operators. The double well case

Abstract : We study a class of PT-symmetric semiclassical Schrodinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is analytic, the eigenvalues stay real for a perturbation of size O(1). We show here, in the double-well case, that the eigenvalues stay real only for exponentially small perturbations, then bifurcate into the complex domain when the perturbation increases and we get precise asymptotic expansions. The proof uses complex WKB-analysis, leading to a fairly explicit quantization condition. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01410406
Contributeur : Imb - Université de Bourgogne <>
Soumis le : mardi 6 décembre 2016 - 15:59:41
Dernière modification le : samedi 18 février 2017 - 01:11:35

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Nawal Mecherout,, Naima Boussekkine,, Thierry Ramond, Johannes Sjoestrand. PT-symmetry and Schrodinger operators. The double well case. Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2016, 289 (7), <http://onlinelibrary.wiley.com/doi/10.1002/mana.201500075/abstract;jsessionid=58CFFB7C7B614FD46FE0071F86070D19.f01t04>. <10.1002/mana.201500075 >. <hal-01410406>

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