Essential implications of similarities in non-Hermitian systems

Anton Montag; Flore K. Kunst

doi:10.1063/5.0206211

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arXiv · 2402.18249

Essential implications of similarities in non-Hermitian systems

Anton Montag·Flore K. Kunst

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Abstract

In this paper, we show that three different generalized similarities enclose all unitary and anti-unitary symmetries that induce exceptional points in lower-dimensional non-Hermitian systems. We prove that the generalized similarity conditions result in a larger class of systems than any class defined by a unitary or anti-unitary symmetry. Further we highlight that the similarities enforce spectral symmetry on the Hamiltonian resulting in a reduction of the codimension of exceptional points. As a consequence we show that the similarities drive the emergence of exceptional points in lower dimensions without the more restrictive need for a unitary and/or anti-unitary symmetry.

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Anton Montag, Flore K. Kunst. 2024-02-28. Essential implications of similarities in non-Hermitian systems. https://doi.org/10.1063/5.0206211

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