Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems
Abstract
We obtain a closed form expression for the energy spectrum of -symmetric superlattice systems with complex potentials of periodic sets of two -potentials in the elementary cell. In the presence of periodic gain and loss we analyzed in detail a diatomic crystal model, varying either the scatterer distances or the potential heights. It is shown that at a certain critical value of the imaginary part of the complex amplitude, topological states depending on the lattice size and the configuration of the unit cell can disappear. This may happened at the -symmetry breaking (exceptional) points.
Keywords
Cite
@article{arxiv.2503.20486,
title = {Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems},
author = {Vladimir Gasparian and Peng Guo and Antonio Pérez Garrido and Esther Jódar},
journal= {arXiv preprint arXiv:2503.20486},
year = {2026}
}
Comments
The title is changed to Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems. Some minor changes in the text to match PRR accepted version