Detection of edge defects by embedded eigenvalues of quantum walks
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866909148234383360 |
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| author | Morioka, Hisashi Segawa, Etsuo |
| author_facet | Morioka, Hisashi Segawa, Etsuo |
| contents | We consider a position-dependent quantum walk on ${\bf Z}$. In particular, we derive a detection method for edge defects by embedded eigenvalues of its time evolution operator. In the present paper, the set of edge defects is that of points in ${\bf Z}$ on which the coin operator is an anti-diagonal matrix. In fact, under some suitable assumptions, the existence of a finite number of edge defects is equivalent to the existence of embedded eigenvalues of the time evolution operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_11742 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Detection of edge defects by embedded eigenvalues of quantum walks Morioka, Hisashi Segawa, Etsuo Spectral Theory Mathematical Physics 47A75, 47A40 We consider a position-dependent quantum walk on ${\bf Z}$. In particular, we derive a detection method for edge defects by embedded eigenvalues of its time evolution operator. In the present paper, the set of edge defects is that of points in ${\bf Z}$ on which the coin operator is an anti-diagonal matrix. In fact, under some suitable assumptions, the existence of a finite number of edge defects is equivalent to the existence of embedded eigenvalues of the time evolution operator. |
| title | Detection of edge defects by embedded eigenvalues of quantum walks |
| topic | Spectral Theory Mathematical Physics 47A75, 47A40 |
| url | https://arxiv.org/abs/1805.11742 |