Physical relevance of time-independent scattering predictions in periodic $\mathcal{PT}$-symmetric chains
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913112731418624 |
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| author | Zheng, Chao |
| author_facet | Zheng, Chao |
| contents | Time-independent scattering methods are widely used to analyze transport in periodic $\mathcal{PT}$-symmetric systems. However, their predictions become unphysical when the system supports time-growing bound states (TGBSs), which manifest as $S$-matrix poles in the first quadrant of the complex wave-number plane. Here, we analytically delineate the region of physical relevance for a $\mathcal{PT}$-symmetric chain of $N$ unit cells with gain/loss strength $γ$. We derive the TGBS onset threshold $γ_c = 2\sin[π/(4N)]$, which scales as $π/(2N)$ for large $N$ and vanishes in the thermodynamic limit. Enlarging the structure thus enriches stationary scattering phenomenology but inevitably triggers TGBSs at weaker gain/loss. Time-dependent wave-packet simulations confirm this analytical boundary quantitatively. Applying this criterion, we show that many previously reported predictions of gain-loss-induced localization, reflectionless transport, and coherent perfect absorbers and lasers in large periodic structures fall outside the physically relevant regime. $S$-matrix pole analysis is therefore an indispensable prerequisite for interpreting time-independent scattering predictions in periodic non-Hermitian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10657 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Physical relevance of time-independent scattering predictions in periodic $\mathcal{PT}$-symmetric chains Zheng, Chao Quantum Physics Optics Time-independent scattering methods are widely used to analyze transport in periodic $\mathcal{PT}$-symmetric systems. However, their predictions become unphysical when the system supports time-growing bound states (TGBSs), which manifest as $S$-matrix poles in the first quadrant of the complex wave-number plane. Here, we analytically delineate the region of physical relevance for a $\mathcal{PT}$-symmetric chain of $N$ unit cells with gain/loss strength $γ$. We derive the TGBS onset threshold $γ_c = 2\sin[π/(4N)]$, which scales as $π/(2N)$ for large $N$ and vanishes in the thermodynamic limit. Enlarging the structure thus enriches stationary scattering phenomenology but inevitably triggers TGBSs at weaker gain/loss. Time-dependent wave-packet simulations confirm this analytical boundary quantitatively. Applying this criterion, we show that many previously reported predictions of gain-loss-induced localization, reflectionless transport, and coherent perfect absorbers and lasers in large periodic structures fall outside the physically relevant regime. $S$-matrix pole analysis is therefore an indispensable prerequisite for interpreting time-independent scattering predictions in periodic non-Hermitian systems. |
| title | Physical relevance of time-independent scattering predictions in periodic $\mathcal{PT}$-symmetric chains |
| topic | Quantum Physics Optics |
| url | https://arxiv.org/abs/2605.10657 |