Hermitian dynamics in a class of pseudo-Hermitian networks

Abstract

We investigate the connection between pseudo-Hermitian and Hermitian descriptions for a lattice, which consists of a set of isomorphic pseudo-Hermitian clusters. We show that such non-Hermitian systems can act as Hermitian systems. This is made possible by considering the dynamics of a state involving the superposition of a single eigenmode of each isomorphic clusters. It still holds when multiple eigenmodes are involved when additional restriction on the state is imposed. This Hermitian dynamics is demonstrated for the case of an exactly solvable PT-symmetric ladder system.

6 pages, 3 figures, accepted for publication in Phys. Rev. A

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• Non-Hermitian tight-binding network engineering
• Inversion symmetric non-Hermitian Chern insulator
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• Hermitian scattering behavior for the non-Hermitian scattering center
• Probability-preserving evolution in a non-Hermitian two-band model
• Quantum battery with non-Hermitian charging
• 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
• Pseudo-Hermiticity protects the energy-difference conservation in the scattering
• $\mathcal{P}\mathcal{T}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities
• Parity-time symmetry under magnetic flux
• Unitary Scattering Protected by Pseudo-Hermiticity
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Transition from degeneracy to coalescence: theorem and applications
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Exceptional points and quantum correlations in precise measurements
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Resonant-amplified and invisible Bragg scattering based on spin coalescing modes
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Coherent confinement and unidirectional dynamics of a wave packet induced by a non-Hermitian Su-Schrieffer-Heeger segment
• Non-Hermitian Aharonov-Bohm Cage