Resonant tunneling effect for quantum walks on directed graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916702030135296 |
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| author | Higuchi, Kenta |
| author_facet | Higuchi, Kenta |
| contents | Quantum walks that depend smoothly on a small parameter $\varepsilon\ge0$ are considered on directed graphs. The asymptotic behavior of the scattering matrix of the quantum walk as $\varepsilon\to+0$ is investigated. It is shown that, in this limit, the scattering matrix does not converge to that for $\varepsilon=0$ at points in the essential spectrum (the unit circle) that are asymptotically approached by a quantum resonance. Furthermore, a phenomenon resembling and extending the resonant tunneling effect is observed by analyzing this discrepancy through resonant states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resonant tunneling effect for quantum walks on directed graphs Higuchi, Kenta Mathematical Physics Spectral Theory Quantum Physics 81U24 (Primary) 47A70, 47D06, 81U26 (Secondary) Quantum walks that depend smoothly on a small parameter $\varepsilon\ge0$ are considered on directed graphs. The asymptotic behavior of the scattering matrix of the quantum walk as $\varepsilon\to+0$ is investigated. It is shown that, in this limit, the scattering matrix does not converge to that for $\varepsilon=0$ at points in the essential spectrum (the unit circle) that are asymptotically approached by a quantum resonance. Furthermore, a phenomenon resembling and extending the resonant tunneling effect is observed by analyzing this discrepancy through resonant states. |
| title | Resonant tunneling effect for quantum walks on directed graphs |
| topic | Mathematical Physics Spectral Theory Quantum Physics 81U24 (Primary) 47A70, 47D06, 81U26 (Secondary) |
| url | https://arxiv.org/abs/2504.15584 |