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

Amina Benbernou (1) , Naima Boussekkine (1) , Nawal Mecherout (1) , Thierry Ramond (2) , Johannes Sjöstrand (3)

1 Fac Sci Exactes & Informat, Univ Mostaganem
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: Eigenvalues; PT-symmetry; Schrödinger operator; Double well

Domaines: Mathématiques [math]; Théorie spectrale [math.SP]; Mathématiques [math]; Physique mathématique [math-ph]

Amina Benbernou, Naima Boussekkine, Nawal Mecherout, Thierry Ramond, Johannes Sjöstrand. Non-Real Eigenvalues for $\mathcal{PT}$-Symmetric Double Wells. Letters in Mathematical Physics, 2016, 106 (12), pp.1817-1835. ⟨10.1007/s11005-016-0852-8⟩. ⟨hal-01446841⟩