Bender-Wu singularities

Abstract

We consider a family of quantum Hamiltonians $H_{\hslash }=-{\hslash }^2(d^2/d{x}^2)+V(x)$, $x\in \mathbb{R},$ $\hslash >0,$ where $V(x)=i(x^3-x)$ is an imaginary double well potential. We prove the existence of infinite eigenvalue crossings with the selection rules of the eigenvalue pairs taking part in a crossing. This is a semiclassical localization effect. The eigenvalues at the crossings accumulate at a critical energy for some of the Stokes lines.

References in corpus (10)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• On the reality of the eigenvalues for a class of PT-symmetric oscillators
• Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian
• Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Hamiltonian is Stieltjes
• Analytic continuation of eigenvalues of a quartic oscillator
• Distributional Borel Summability of Odd Anharmonic Oscillators
• The spectrum of the cubic oscillator
• PT-symmetric operators and metastable states of the 1D relativistic oscillators
• Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families
• Level Crossings in a PT-symmetric Double Well

Cited by in corpus (1)

• Relativistic levels of mesic atoms