The phenomenon of revivals on complex potential Schrödinger's equation

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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.
Original languageEnglish
JournalZeitschrift für Analysis und ihre Anwendungen
Early online date30 May 2024
DOIs
Publication statusE-pub ahead of print - 30 May 2024

Keywords

  • math.AP
  • math-ph
  • math.MP
  • math.SP

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