Cryptohermitian Hamiltonians on graphs. II. Hermitizations
arXiv:1101.1015 · doi:10.1007/s10773-011-0671-8
Abstract
Non-hermitian quantum graphs possessing real (i.e., in principle, observable) spectra are studied via their discretization. The discretized Hamiltonians are assigned, constructively, an elementary pseudometric and/or a more complicated metric. Both these constructions make the Hamiltonian Hermitian, respectively, in an auxiliary (Krein or Pontryagin) vector space or in a less friendly (but more useful) Hilbert space of quantum mechanics.
25 pp., 2 figs
References in corpus (10)
- Making Sense of Non-Hermitian Hamiltonians
- Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
- The ODE/IM Correspondence
- Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
- Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
- Complex Lagrangians and phantom cosmology
- A Note on Quantum Field Theories with a Minimal Length Scale
- Matching method and exact solvability of discrete PT-symmetric square wells
- Non-Hermitian quantum mechanics in non-commutative space
- Cryptohermitian Hamiltonians on graphs