PT-symmetric trimer systems

We studied parity-time (PT) symmetric trimer systems that feature open and closed boundaries. The exceptional point is three-state coalescence at zero energy because of chiral symmetry in the open trimer; however, two-state coalescence appears in the closed trimer affected by the magnetic flux enclosed, which suppresses the PT transition. Dynamics at the phase transition point were also qualitatively studied. For three-state coalescence, the probability of an initial state increases in a power law. The highest order is four; however, it can be reduced to two for the state that is only relevant to one associated state. For two-state coalescence in the trimer ring, we found four typical dynamical behaviors of state probability: (i) unchanged, (ii) oscillation, (iii) quadratic increase, and (iv) quadratic increase with oscillation. The scattering properties of the trimer systems were also studied, particularly, asymmetric wave emissions at spectral singularities