Exceptional-Point Dynamics

TL;DR

This paper systematically investigates the dynamics at exceptional points in non-Hermitian systems, revealing polynomial growth behaviors and providing models to understand and utilize these phenomena for advanced device engineering.

Contribution

It establishes pseudo-completeness relations at EPs using generalized eigenstates, addressing both single and multiple EPs, and demonstrates their dynamical behaviors with PH-compliant models.

Findings

EP dynamics can show polynomial growth over time

Long-term evolution can be dominated by coalescing eigenstates

Models demonstrate potential applications of EP dynamics

Abstract

Exceptional points (EPs) play a vital role in non-Hermitian (NH) systems, driving unique dynamical phenomena and promising innovative applications. However, the NH dynamics at EPs remains obscure due to the incomplete biorthogonal eigenspaces of defective NH Hamiltonians and thus is often avoided. In this manuscript, we systematically establish pseudo-completeness relations at EPs by employing all available generalized eigenstates, where both single and multiple arbitrary-order EPs embracing degenerate scenarios are addressed, to unveil EP dynamics. We reveal that depending on EP order and initial conditions, the EP dynamics is characterized by a \emph{polynomial growth over time} of coalescing eigenstates or their superposition, which will dominate long-term evolution despite real spectra protected by pseudo-Hermiticity (PH), or can also become unitary. We further introduce two PH-compliant NH models to demonstrate these EP dynamics and explore their applications. This work completes the dynamical investigation of NH physics, offers valuable insights into the nonunitary evolution at EPs, and further lays the foundation for engineering and exploiting EP-related devices and technologies.