We study the $\mathcal{PT} $-symmetry breaking for the scattering problem ina one-dimensional (1D) non-Hermitian tight-binding lattice model with balancedgain and loss distributed on two adjacent sites. In the scattering process thesystem undergoes a transition from the exact $\mathcal{PT} $-symmetry phase tothe phase with spontaneously breaking $\mathcal{PT} $-symmetry as the amplitudeof complex potentials increases. Using the S-matrix method, we derive an exactdiscriminant, which can be used to distinguish different symmetry phases, andanalytically determine the exceptional point for the symmetry breaking. In the$\mathcal{PT} $-symmetry breaking region, we also confirm the appearance of theunique feature, i.e., the coherent perfect absorption Laser, in this simplenon-Hermitian lattice model. The study of the scattering problem of such asimple model provides an additional way to unveil the physical effect ofnon-Hermitian $\mathcal{PT} $-symmetric potentials.
展开▼
