A physical interpretation for the non-Hermitian Hamiltonian

Abstract

We explore a way of finding the link between a non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of Bethe Ansatz solutions for a class of non-Hermitian Hamiltonians and the scattering problems for the corresponding Hermitian Hamiltonians. It is shown that a scattering state of an arbitrary Hermitian lattice embedded in a chain as the scattering center shares the same wave function with the corresponding non-Hermitian tight binding lattice, which consists of the Hermitian lattice with two additional on-site complex potentials, no matter the non-Hermitian is broken PT symmetry or even non-PT. An exactly solvable model is presented to demonstrate the main points of this article.

8 pages, 3 figures

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Cited by in corpus (21)

• Perspective on topological states of non-Hermitian lattices
• Topological phases in Kitaev chain with imbalanced pairing
• High-order exceptional points in supersymmetric arrays
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Probability-preserving evolution in a non-Hermitian two-band model
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Simple harmonic oscillation in non-Hermitian SSH chain at exceptional point
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Coalescing Majorana edge modes in non-Hermitian PT-symmetric Kitaev chain
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Hidden exceptional point, localization-delocalization phase transition in Hermitian bosonic Kitaev model
• Topological phase in Kitaev chain with spatially separated pairing processes
• Resonant-amplified and invisible Bragg scattering based on spin coalescing modes
• Supersymmetry of $\mathcal{P}\mathcal{T}$- symmetric tridiagonal Hamiltonians
• Coalescing hardcore-boson condensate states with nonzero momentum
• Parallel dynamics between non-Hermitian and Hermitian systems
• Exceptional spectrum and dynamic magnetization
• Higher order coherence as witness of exceptional point in Hermitian bosonic Kitaev dimer
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes