2025/02/28 by Julius Kullig, Jan Wiersig · 1 voice · 2 citations
Mathematics · Physics and Astronomy · #Geometry #Hermitian matrix #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Point (geometry) #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Statistical physics #Theoretical physics
paper · pdf · doi:10.1103/physrevresearch.7.013223
published in Physical Review Research 7(1) (American Physical Society)
openalex publication_date 2025/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Exceptional points are spectral degeneracies in open systems, which have attracted considerable attention in recent years. One reason for the attention is that physical systems with an exceptional point exhibit a strong spectral response to perturbations. This response can be quantified by a single quantity known as the spectral response strength. Up to now, the theory for the spectral response strength is restricted to effective non-Hermitian Hamiltonians acting on a finite-dimensional Hilbert space, which often appear naturally within coupled-mode theory. We introduce here a scheme for the computation of the spectral response strength directly from numerical results of wave simulations, which correspond to an infinite Hilbert-space dimension. Our approach is based on the relation of the spectral response strength to the Petermann factors of eigenstates in a system near the exceptional point. To illustrate our theory, we consider three different photonic systems: a microring dimer, waveguide-coupled microrings, and a weakly deformed microdisk. A comparison to results provided by effective Hamiltonians based on coupled-mode theory and perturbation theory demonstrates very good agreement.