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

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

2010-03-19

arxiv.org/abs/1003.3738v2

J. Phys. A: Math. Theor. 43 (2010) 335303

Physics

Quantum Physics

17 pp., 9 figures, published version

Scientific paper

10.1088/1751-8113/43/33/335303

Toy quantum Hamiltonians $H\neq H^\dagger$ 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 $H= H^\ddagger$ 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.

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