Related papers: Extremely broken generalized $\mathcal{PT}$ symmetry

Extremely broken generalized $\mathcal{PT}$ symmetry

URL: http://arxiv.org/abs/2206.11859v3
Date: Wed, 12 Jul 2023 14:06:07 GMT
Title: Extremely broken generalized $\mathcal{PT}$ symmetry
Authors: Francisco M. Fern\'andez
Abstract summary: We discuss some simple H"uckel-like matrix representations of non-Hermitian operators with antiunitary symmetries. One of them exhibits extremely broken antiunitary symmetry because of the degeneracy of the operator in the Hermitian limit.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We discuss some simple H\"uckel-like matrix representations of non-Hermitian operators with antiunitary symmetries that include generalized $\mathcal{PT}$ (parity transformation followed by time-reversal) symmetry. One of them exhibits extremely broken antiunitary symmetry (complex eigenvalues for all nontrivial values of the model parameter) because of the degeneracy of the operator in the Hermitian limit. These examples illustrate the effect of point-group symmetry on the spectrum of the non-Hermitian operators. We construct the necessary unitary matrices by means of simple graphical representations of the non-Hermitian operators.

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