Physics counterpart of the PT non-hermitian tight-binding chain

Abstract

We explore an alternative way of finding the link between a PT non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of the scattering problem for an imaginary potential and its time reversal process, it is shown that any real-energy eigenstate of a PT tight-binding lattice with on-site imaginary potentials shares the same wave function with a resonant transmission state of the corresponding Hermitian lattice embedded in a chain. It indicates that the PT eigenstate of a PT non-Hermitian Hamiltonian has connection to the resonance transmission state of the extended Hermitian Hamiltonian.

6 pages, 3 figures

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Cited by in corpus (27)

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• Spontaneous PT symmetry breaking and quantum phase transitions in dimerized spin chains
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Flat band in two-dimensional non-Hermitian optical lattices
• Graphene, Lattice QFT and Symmetries
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• Wave emission and absorption at spectral singularities
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Probability-preserving evolution in a non-Hermitian two-band model
• Quantum battery with non-Hermitian charging
• Non-Hermitian interferometer: Unidirectional amplification without distortion
• Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity
• Exceptional points in oligomer chains
• Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric flat band lattice
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
• Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Robust incoherent perfect absorption
• Berry curvature inside parity-time-symmetry protected exceptional surface
• 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
• Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems
• Coalescing hardcore-boson condensate states with nonzero momentum
• Building ground states of Hubbard model by time-ordered bound-pair injection
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes
• Higher order coherence as witness of exceptional point in Hermitian bosonic Kitaev dimer