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# Complex symmetric Hamiltonians and exceptional points of order four and five

preprint

posted on 2023-11-30, 06:11 authored by Miloslav ZnojilIn the broad context of physics ranging from classical experimental optics to quantum mechanics of unitary as well as non-unitary systems there emerge interesting phenomena related to the presence of the so called Kato's exceptional points in the space of parameters. An elementary linear-algebraic method of their localization is proposed and applied to the class of tridiagonal $N$ by $N$ complex symmetric toy-model generators of evolution $H=H(\gamma)$. The implementation of the method is shown to provide new models with the exceptional points $\gamma=\gamma^{(EP)}$ of higher orders. Two distinct areas of applicability are expected to lie (1) in quantum mechanics of non-Hermitian (open as well as closed) systems, and (2) in the experiments using the coupled classical optical waveguides simulating the EP-related effects in the laboratory.