Graph-theoretical approach to the eigenvalue spectrum of perturbed higher-order exceptional points

• URL: http://arxiv.org/abs/2409.13434v1
• Date: Fri, 20 Sep 2024 11:56:15 GMT
• Title: Graph-theoretical approach to the eigenvalue spectrum of perturbed higher-order exceptional points
• Authors: Daniel Grom, Julius Kullig, Malte Röntgen, Jan Wiersig,
• Abstract summary: We advocate a graph-theoretical perspective that contributes to the understanding of perturbative effects on the eigenvalue spectrum of higher-order exceptional points. We consider an illustrative example, a system of microrings coupled by a semi-infinite waveguide with an end mirror.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exceptional points are special degeneracy points in parameter space that can arise in (effective) non-Hermitian Hamiltonians describing open quantum and wave systems. At an n-th order exceptional point, n eigenvalues and the corresponding eigenvectors simultaneously coalesce. These coalescing eigenvalues typically exhibit a strong response to small perturbations which can be useful for sensor applications. A so-called generic perturbation with strength $\epsilon$ changes the eigenvalues proportional to the n-th root of $\epsilon$. A different eigenvalue behavior under perturbation is called non-generic. An understanding of the behavior of the eigenvalues for various types of perturbations is desirable and also crucial for applications. We advocate a graph-theoretical perspective that contributes to the understanding of perturbative effects on the eigenvalue spectrum of higher-order exceptional points, i.e. n > 2. To highlight the relevance of non-generic perturbations and to give an interpretation for their occurrence, we consider an illustrative example, a system of microrings coupled by a semi-infinite waveguide with an end mirror. Furthermore, the saturation effect occurring for cavity-selective sensing in such a system is naturally explained within the graph-theoretical picture.

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