Complex translation methods and its application to resonances for quantum walks
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929286825377792 |
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| author | Higuchi, Kenta Morioka, Hisashi |
| author_facet | Higuchi, Kenta Morioka, Hisashi |
| contents | In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_00962 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complex translation methods and its application to resonances for quantum walks Higuchi, Kenta Morioka, Hisashi Spectral Theory Mathematical Physics Analysis of PDEs 81U24, 47A75 In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier. |
| title | Complex translation methods and its application to resonances for quantum walks |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs 81U24, 47A75 |
| url | https://arxiv.org/abs/2307.00962 |