Exponentially decaying velocity bounds of quantum walks in periodic fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917566841094144 |
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| author | Abdul-Rahman, Houssam Stolz, Günter |
| author_facet | Abdul-Rahman, Houssam Stolz, Günter |
| contents | We consider a class of discrete-time one-dimensional quantum walks, associated with CMV unitary matrices, in the presence of a local field. This class is parametrized by a transmission parameter $t\in[0,1]$. We show that for a certain range for $t$, the corresponding asymptotic velocity can be made arbitrarily small by introducing a periodic local field with a sufficiently large period. In particular, we prove an upper bound for the velocity of the $n$-periodic quantum walk that is decaying exponentially in the period length $n$. Hence, localization-like effects are observed even after a long number of quantum walk steps when $n$ is large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01869 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exponentially decaying velocity bounds of quantum walks in periodic fields Abdul-Rahman, Houssam Stolz, Günter Mathematical Physics Quantum Physics We consider a class of discrete-time one-dimensional quantum walks, associated with CMV unitary matrices, in the presence of a local field. This class is parametrized by a transmission parameter $t\in[0,1]$. We show that for a certain range for $t$, the corresponding asymptotic velocity can be made arbitrarily small by introducing a periodic local field with a sufficiently large period. In particular, we prove an upper bound for the velocity of the $n$-periodic quantum walk that is decaying exponentially in the period length $n$. Hence, localization-like effects are observed even after a long number of quantum walk steps when $n$ is large. |
| title | Exponentially decaying velocity bounds of quantum walks in periodic fields |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2302.01869 |