Symmetry and degeneracy, exceptional point and coalescence: a pedagogical approach

Francisco M. Fernández

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arXiv · 2108.08287

Symmetry and degeneracy, exceptional point and coalescence: a pedagogical approach

Francisco M. Fernández

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Abstract

We show a parameter-dependent $3\times 3$ non-Hermitian matrix that exhibits both degeneracy and coalescence of eigenvalues at an exceptional point (Hermitian and non-Hermitian degeneracies). This simple non-Hermitian model is suitable for the discussion of those concepts in an undergraduate or graduate course on quantum-mechanics. We also study the symmetry group responsible for the degeneracy.

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Francisco M. Fernández. 2021-08-17. Symmetry and degeneracy, exceptional point and coalescence: a pedagogical approach. https://arxiv.org/abs/2108.08287

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