Limiting distributions of ergodic continuous-time quantum walks on periodic graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915191762976768 |
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| author | de Monvel, Anne Boutet S., Kiran Kumar A. Sabri, Mostafa |
| author_facet | de Monvel, Anne Boutet S., Kiran Kumar A. Sabri, Mostafa |
| contents | In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk explicitly. We uncover interesting behavior where in some families, the walk is ergodic in both horizontal and sectional directions, while in others, ergodicity only holds in the horizontal (large N) direction. We compare this to the limiting distribution of classical random walks on the same graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limiting distributions of ergodic continuous-time quantum walks on periodic graphs de Monvel, Anne Boutet S., Kiran Kumar A. Sabri, Mostafa Mathematical Physics Spectral Theory 47A35, 58J51 In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk explicitly. We uncover interesting behavior where in some families, the walk is ergodic in both horizontal and sectional directions, while in others, ergodicity only holds in the horizontal (large N) direction. We compare this to the limiting distribution of classical random walks on the same graphs. |
| title | Limiting distributions of ergodic continuous-time quantum walks on periodic graphs |
| topic | Mathematical Physics Spectral Theory 47A35, 58J51 |
| url | https://arxiv.org/abs/2503.08595 |