$\mathcal{P}\mathcal{T}$ symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

Abstract

We study the $\mathcal{P}\mathcal{T}$-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact $\mathcal{P}\mathcal{T}$-symmetry phase to the phase with spontaneously breaking $\mathcal{P}\mathcal{T}$-symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for the symmetry breaking. In the $\mathcal{P}\mathcal{T}$-symmetry breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption Laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric potentials.

6 pages, 3 figures

References in corpus (9)

• Coherent Perfect Absorbers: Time-reversed Lasers
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• PT-Symmetric Phonon Laser
• Topological invariance and global Berry phase in non-Hermitian systems
• Invisibility and PT-symmetry
• Topological phase in a non-Hermitian PT symmetric system
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Non-Hermitian spectra and Anderson localization
• Coherent perfect absorption with and without lasing in complex potentials

Cited by in corpus (8)

• PT-symmetric scattering in flow duct acoustics
• $\mathcal{P}\mathcal{T}$-symmetric slowing-down of decoherence
• Non-Hermitian scattering on a tight-binding lattice
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Non-Hermitian noncommutative quantum mechanics
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Dynamical evolution of an effective two-level system with PT symmetry
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states