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

TL;DR

This paper investigates non-Hermitian quantum graphs with real spectra, revealing that graph topology can induce nonperturbative energy features in strong-coupling regimes.

Contribution

It introduces a framework for analyzing non-Hermitian Hamiltonians on quantum graphs with real spectra, emphasizing the role of topology and a nontrivial metric.

Findings

Graph topology influences nonperturbative energy features

Non-Hermitian Hamiltonians can have real spectra on quantum graphs

Discrete models reveal topology-related spectral properties

Abstract

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.