Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime

Abstract

Toy quantum Hamiltonians $H\ne H^{†}$ with real spectra are considered as living on graphs $\mathbb{G}$ which only differ from the standard real line $\mathbb{R}$ locally, on a microscopic fundamental-length scale. In terms of a nontrivial metric the "hidden Hermiticity" property $H=H^{‡}$ is postulated. Our calculations of the energies (based on a discretization of $\mathbb{G}$) indicate that the nontriviality of the topology of the graph may be responsible for certain nonperturbative features of the energies.

Comments: 17 pp., 9 figures, published version