Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909001945448448 |
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| author | Gasparian, Vladimir Guo, Peng Garrido, Antonio Pérez Jódar, Esther |
| author_facet | Gasparian, Vladimir Guo, Peng Garrido, Antonio Pérez Jódar, Esther |
| contents | We obtain a closed form expression for the energy spectrum of $\mathcal{P}\mathcal{T}$-symmetric superlattice systems with complex potentials of periodic sets of two $δ$-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 $\mathcal{PT}$-symmetry breaking (exceptional) points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems Gasparian, Vladimir Guo, Peng Garrido, Antonio Pérez Jódar, Esther Mesoscale and Nanoscale Physics Other Condensed Matter We obtain a closed form expression for the energy spectrum of $\mathcal{P}\mathcal{T}$-symmetric superlattice systems with complex potentials of periodic sets of two $δ$-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 $\mathcal{PT}$-symmetry breaking (exceptional) points. |
| title | Characteristic determinant approach to the spectrum of one-dimensional $\mathcal{P}\mathcal{T}$-symmetric systems |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2503.20486 |