High-Order Exceptional Points in Diffusive Systems: Robust APT Symmetry Against Perturbation and Phase Oscillation at APT Symmetry Breaking

Abstract

In non-Hermitian systems with the Hamiltonians obeying parity-time (PT) symmetry, exploring the counterintuitive physics induced by degeneracies known as exceptional points (EPs) provides unprecedented ways to control energy flow. Recently, there are growing interests in bridging wave systems and diffusive systems, where anti-parity-time (APT) symmetry is demonstrated in diffusive systems. In this work, we start from the thermal energy transfer in a four-channel coupling model with the background flow velocities in adjacent channels opposite. A third order EP exists in this system, where temperature profiles in the moving channels are static in the APT symmetric phase (flow velocities below a threshold υEP at the EP), and the profiles begin to dynamically evolve in the APT broken phase (> υEP). By introducing a velocity perturbation into the background flow at the third order EP (υEP ± ∆υ), we find APT symmetry keeps robust with the phases of temperature profiles in adjacent channels relatively static or locked. When ∆υ is increased above a threshold (another EP), the APT symmetry is breaking with a transition from phase locking to phase oscillation, regardless of initial conditions. This work unveils rich physics in convectively coupled diffusive systems and offers us new prospects for the control of complex thermal fields.