Anti-parity-time symmetric phase transition in diffusive systems

Parity-time (PT) symmetry/anti-parity-time (APT) symmetry in non-Hermitian systems reveal profound physics and spawn intriguing effects. Recently, it has been introduced into diffusive systems together with the concept of exceptional points (EPs) from quantum mechanics and the wave systems. With the aid of convection, we can generate complex thermal conductivity and imitate various wavelike dynamics in heat transfer, where heat flow can be "stopped" or moving against the background motion. Non-Hermitian diffusive systems offer us a new platform to investigate the heat wave manipulation. In this review, we first introduce the construction of APT symmetry in a simple double-channel toy model. Then we show the phase transition around the EP. Finally, we extend the double-channel model to the four-channel one for showing the high-order EP and the associated phase transition. In a general conclusion, the phase difference of adjacent channels is always static in the APT symmetric phase, while it dynamically evolves or oscillates when the APT symmetry is broken. (topical review)