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.

17 pp., 9 figures, published version

References in corpus (17)

• Making Sense of Non-Hermitian Hamiltonians
• The ODE/IM Correspondence
• Time-dependent version of cryptohermitian quantum theory
• Time evolution of non-Hermitian Hamiltonian systems
• Scattering theory with localized non-Hermiticities
• Perturbation theory of PT-symmetric Hamiltonians
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• A Positive-Definite Scalar Product for Free Proca Particle
• From PT-symmetric quantum mechanics to conformal field theory
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Matrix Hamiltonians with an algebraic guarantee of unbroken PT-symmetry
• On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator
• Solvable relativistic quantum dots with vibrational spectra
• Particles versus fields in PT-symmetrically deformed integrable systems
• Classification of the conditionally observable spectra exhibiting central symmetry
• Spectra of PT-symmetric Hamiltonians on Tobogganic Contours
• Conditional observability versus self-duality in a schematic model

Cited by in corpus (9)

• Quantum catastrophes: a case study
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Discrete quantum square well of the first kind
• Decays of degeneracies in PT-symmetric ring-shaped lattices
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Quantum star-graph analogues of PT-symmetric square wells
• N-site-lattice analogues of $V(x)=i{x}^3$
• Cryptohermitian Hamiltonians on graphs
• Cryptohermitian Hamiltonians on graphs. II. Hermitizations