PT-symmetric trimer systems

TL;DR

This paper investigates PT-symmetric trimer systems with open and closed boundaries, analyzing exceptional points, coalescence phenomena, dynamics at phase transitions, and scattering properties, revealing complex behaviors and symmetry effects.

Contribution

It provides new insights into the coalescence phenomena and dynamical behaviors in PT-symmetric trimers, including effects of boundary conditions and magnetic flux.

Findings

Three-state coalescence at zero energy due to chiral symmetry

Two-state coalescence in closed trimers influenced by magnetic flux

Four types of dynamical behaviors at phase transition points

Abstract

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