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PT-symmetry and Schr\"odinger operators. The double well case by Mecherout, Nawal; Boussekkine, Naima; Ramond, Thierry; Sjoestrand, Johannes is a scholarly article available to read on EtoBox.

What is PT-symmetry and Schr\"odinger operators. The double well case about?

We study a class of PT-symmetric semiclassical Schr\"odinger 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 \cite{BoMe14} 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.

Author

Mecherout, Nawal; Boussekkine, Naima; Ramond, Thierry; Sjoestrand, Johannes

Published

2015

Language

EN