On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation

Abstract

We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a Hermitian, positive-definite, diagonal operator. We show that there is an important difference between open boundary conditions and periodic ones. We illustrate the theoretical results by means of two simple, widely used, models.

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• Scattering theory with localized non-Hermiticities
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Non-Hermitian skin effect as an impurity problem
• Gegenbauer-solvable quantum chain model
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Conditional observability
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Spectra, eigenstates and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric ring

Cited by in corpus (5)

• Complex tridiagonal quantum Hamiltonians and matrix continued fractions
• Quantum singularities in a solvable toy model
• Few-grid-point simulations of Big Bang singularity in quantum cosmology
• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models
• Extremely broken generalized $\mathcal{P}\mathcal{T}$ symmetry