Dynamical system approach to the spectral instability of open systems under localised perturbations

Migration plot of the complex frequencies (quasinormal modes) of a toy model black hole. As the strength of the perturbation, ϵ increases, the resonances migrate along trajectories shown as solid purple lines, ultimately towards the attracting points marked as open black circles. The unperturbed spectrum is shown with filled black circles. The repelling points are marked with black crosses, and the integral curves that move away from (towards) these points as ϵ increases are shown as dotted blue (red) lines.

Abstract: Open systems are ubiquitous in physics, arising whenever energy, matter, or information is exchanged with an environment and their spectral properties play a central role in determining dynamical behaviour across a wide range of disciplines. It has been shown that the spectral properties of open systems can be extremely sensitive to perturbations, leading to the phenomena of spectral instability: a small modification of the system may change drastically its resonant spectrum. In this talk, we’ll investigate how localized perturbations affect the complex spectrum of resonances of one-dimensional open systems. We’ll reveal that the spectrum deforms in a smooth and continuous manner, tracing well-defined trajectories in the complex plane. Adopting a dynamical systems perspective, we’ll show that those trajectories are governed by attracting and repelling spectral points that depend only on the unperturbed system. The presented framework provides a unified and intuitive interpretation of spectral instabilities in open systems and is broadly applicable to resonant phenomena in wave physics. 

‼️ Le séminaire peut être suivi en ligne suivant le lien : https://univ-amu-fr.zoom.us/j/95011527683?pwd=bTeNvaaZY75buaa7bRL0pcucXSASm7.1

Le mardi 3 février 2026 à 11h00 / Amphithéâtre François Canac, LMA

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