Oral: Exceptional degeneracies and their non-Abelian topology in non-Hermitian systems

Defective spectral degeneracy, known as exceptional point (EP), lies at the heart of various intriguing phenomena in optics, acoustics, and other nonconservative systems. In this presentation, we provide a topological classification of isolated exceptional degeneracies based on homotopy theory. We then put forward a universal non-Abelian conservation rule governing the collective behaviors (e.g., annihilation, coalescence, braiding, etc.) in generic non-Hermitian systems and uncover several counterintuitive phenomena. We demonstrate that two EPs with opposite charges (even the pairwise created) do not necessarily annihilate, depending on how they approach each other. Furthermore, we unveil that the conservation rule imposes strict constraints on the permissible exceptional-line configurations. It excludes structures like Hopf link yet permits novel staggered rings composed of noncommutative exceptional lines. These intriguing phenomena are illustrated by concrete models which could be readily implemented in platforms like coupled acoustic cavities, optical waveguides, and ring resonators. Our findings lay the cornerstone for a comprehensive understanding of the exceptional non-Abelian topology and shed light on the versatile manipulations and applications based on exceptional degeneracies in nonconservative systems.