The phenomenon of revivals on complex potential Schrödinger's equation

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Boulton, Lyonell, Farmakis, George, Pelloni, Beatrice
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.06.2024
Subjects
Mathematical analysis
Schrodinger equation
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Summary: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 Schr\"odinger'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.
ISSN:2331-8422
DOI:10.48550/arxiv.2308.09961