Non-real Eigenvalues for PT-Symmetric Double Wells

Abstract

We study small, 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.

References in corpus (3)

• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• Perturbation theory of PT-symmetric Hamiltonians
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum