The analytically tractable zoo of similarity-induced exceptional structures

2025/08/04 by Anton Montag, Montag, Anton, Jordan Isaacs +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Optics (physics.optics) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2508.02565

openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Exceptional points (EPs) are non-Hermitian spectral degeneracies marking a simultaneous coalescence of eigenvalues and eigenvectors. Despite the fact that multiband n-fold EPs (EPns) generically emerge as special points on manifolds of EPms, where m

Citations

• Third-Order Exceptional Point in Non-Hermitian Spin-Orbit-Coupled cold atoms
• Abelian Spectral Topology of Multifold Exceptional Points
• The non-Hermitian skin effect: A perspective
• Third-order exceptional line in a nitrogen-vacancy spin system
• Non-Hermitian Optical Parametric Systems with Anti-parity-time Symmetry
• Non-Hermitian Topoelectrical Circuits: Expedient Tools for Topological State Engineering with Gain-Loss Modulation
• Tidal surface states as fingerprints of non-Hermitian nodal knot metals
• A Galileon Primer
• Classification of topological insulators and superconductors in three spatial dimensions
• Physics of Nonhermitian Degeneracies

Related

• Universal Topology of Exceptional Points in Nonlinear Non-Hermitian Systems
• General Exceptional Points
• Exceptional deficiency of non-Hermitian systems: high-dimensional coalescence and dynamics
• Abelian Spectral Topology of Multifold Exceptional Points
• Global and Local Aspects of Exceptional Point