The phenomenon of revivals on complex potential Schrödinger's equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910483091554304 |
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| author | Boulton, Lyonell Farmakis, George Pelloni, Beatrice |
| author_facet | Boulton, Lyonell Farmakis, George Pelloni, Beatrice |
| contents | The mysterious phenomena of revivals in linear dispersive periodic equations was discovered first experimentally in optics in the 19th century, then rediscovered several times by theoretical and experimental investigations. While the term has been used systematically and consistently by many authors, there is no consensus on a rigorous definition. In this paper, we describe revivals modulo a regularity condition in a large class of Schrödinger's equations with complex bounded potentials. As we show, at rational times the solution is given explicitly by finite linear combinations of translations and dilations of the initial datum, plus an additional continuous term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09961 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The phenomenon of revivals on complex potential Schrödinger's equation Boulton, Lyonell Farmakis, George Pelloni, Beatrice Analysis of PDEs Mathematical Physics Spectral Theory The mysterious phenomena of revivals in linear dispersive periodic equations was discovered first experimentally in optics in the 19th century, then rediscovered several times by theoretical and experimental investigations. While the term has been used systematically and consistently by many authors, there is no consensus on a rigorous definition. In this paper, we describe revivals modulo a regularity condition in a large class of Schrödinger's equations with complex bounded potentials. As we show, at rational times the solution is given explicitly by finite linear combinations of translations and dilations of the initial datum, plus an additional continuous term. |
| title | The phenomenon of revivals on complex potential Schrödinger's equation |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2308.09961 |