Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917605447565312 |
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| author | Loebens, Newton |
| author_facet | Loebens, Newton |
| contents | We study continuous-time open quantum walks in one dimension through a matrix representation, focusing on nearest-neighbor transitions for which an associated weight matrix exists. Statistics such as site recurrence are studied in terms of matrix-valued orthogonal polynomials and explicit calculations are obtained for classes of Lindblad generators that model quantum versions of birth-death processes. Emphasis is given to the technical distinction between the cases of a finite or infinite number of vertices. Recent results for open quantum walks are adapted in order to apply the folding trick to continuous-time birth-death chains on the integers. Finally, we investigate the matrix-valued Stieltjes transform associated to the weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16366 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators Loebens, Newton Quantum Physics We study continuous-time open quantum walks in one dimension through a matrix representation, focusing on nearest-neighbor transitions for which an associated weight matrix exists. Statistics such as site recurrence are studied in terms of matrix-valued orthogonal polynomials and explicit calculations are obtained for classes of Lindblad generators that model quantum versions of birth-death processes. Emphasis is given to the technical distinction between the cases of a finite or infinite number of vertices. Recent results for open quantum walks are adapted in order to apply the folding trick to continuous-time birth-death chains on the integers. Finally, we investigate the matrix-valued Stieltjes transform associated to the weights. |
| title | Continuous-time open quantum walks in one dimension: matrix-valued orthogonal polynomials and Lindblad generators |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2311.16366 |