Directional Ballistic Transport for Partially Periodic Schrödinger Operators on $\mathbb{Z}^2$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915724295929856 |
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| author | Black, Adam Damanik, David Malinovitch, Tal Young, Giorgio |
| author_facet | Black, Adam Damanik, David Malinovitch, Tal Young, Giorgio |
| contents | We study the transport properties of Schrödinger operators on $\mathbb{Z}^2$ with potentials that are periodic in one direction and compactly supported in the other. Such systems are known to produce surface states that are weakly confined near the support of the potential. We demonstrate that surface states exhibit what we describe as directional ballistic transport, characterized by a strong form of ballistic transport along the periodic direction and its absence in the compactly supported one. By showing that the scattering states exhibit ballistic transport, we obtain ballistic transport for a dense subset of all of $\ell^2(\mathbb {Z} ^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08612 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Directional Ballistic Transport for Partially Periodic Schrödinger Operators on $\mathbb{Z}^2$ Black, Adam Damanik, David Malinovitch, Tal Young, Giorgio Spectral Theory Mathematical Physics We study the transport properties of Schrödinger operators on $\mathbb{Z}^2$ with potentials that are periodic in one direction and compactly supported in the other. Such systems are known to produce surface states that are weakly confined near the support of the potential. We demonstrate that surface states exhibit what we describe as directional ballistic transport, characterized by a strong form of ballistic transport along the periodic direction and its absence in the compactly supported one. By showing that the scattering states exhibit ballistic transport, we obtain ballistic transport for a dense subset of all of $\ell^2(\mathbb {Z} ^2)$. |
| title | Directional Ballistic Transport for Partially Periodic Schrödinger Operators on $\mathbb{Z}^2$ |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2311.08612 |