Dispersive effects for the Schrödinger equation on finite metric graphs with infinite ends
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910600381071360 |
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| author | Mehmeti, Felix Ali Ammari, Kaïs Nicaise, Serge |
| author_facet | Mehmeti, Felix Ali Ammari, Kaïs Nicaise, Serge |
| contents | We study the free Schrödinger equation on finite metric graphs with infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$ time decay rate at least $t^{-1/2}$. These conditions allow certain metric graphs with circles and/or with commensurable lengths of the bounded edges. Further we study the dynamics of the probability flow between the bounded sub-graph and the unbounded ends. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16628 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dispersive effects for the Schrödinger equation on finite metric graphs with infinite ends Mehmeti, Felix Ali Ammari, Kaïs Nicaise, Serge Analysis of PDEs 34B45, 47A60, 34L25, 35B20, 35B40 We study the free Schrödinger equation on finite metric graphs with infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$ time decay rate at least $t^{-1/2}$. These conditions allow certain metric graphs with circles and/or with commensurable lengths of the bounded edges. Further we study the dynamics of the probability flow between the bounded sub-graph and the unbounded ends. |
| title | Dispersive effects for the Schrödinger equation on finite metric graphs with infinite ends |
| topic | Analysis of PDEs 34B45, 47A60, 34L25, 35B20, 35B40 |
| url | https://arxiv.org/abs/2310.16628 |