Bender-Wu singularities

Riccardo Giachetti; Vincenzo Grecchi

doi:10.1063/1.4972290

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arXiv · 1607.00190

Bender-Wu singularities

Riccardo Giachetti·Vincenzo Grecchi

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Abstract

We consider a family of quantum Hamiltonians $H_\hbar=-\hbar^2\,(d^2\!/dx^2) +V(x)$, $x\in\mathbb{R},$ $\hbar>0,$ 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.

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Riccardo Giachetti, Vincenzo Grecchi. 2016-07-01. Bender-Wu singularities. https://doi.org/10.1063/1.4972290

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