The phenomenon of revivals on complex potential Schrödinger’s equation

Journal article


Boulton, L., Farmakis, G. and Pelloni, B. (2024). The phenomenon of revivals on complex potential Schrödinger’s equation. Zeitschrift für Analysis und ihre Anwendungen. 43 (3), pp. 401-416. https://doi.org/10.4171/zaa/1762
AuthorsBoulton, L., Farmakis, G. and Pelloni, B.
Abstract

The mysterious phenomenon 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.

Year2024
JournalZeitschrift für Analysis und ihre Anwendungen
Journal citation43 (3), pp. 401-416
PublisherEuropean Mathematical Society - EMS - Publishing House GmbH
ISSN0232-2064
1661-4534
Digital Object Identifier (DOI)https://doi.org/10.4171/zaa/1762
Web address (URL)https://ems.press/journals/zaa/articles/14297854
Publication dates
Print30 May 2024
Publication process dates
Deposited19 Aug 2024
Publisher's version
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Open
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