The phenomenon of revivals on complex potential Schr\"odinger's equation
Abstract
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.
Keywords
Cite
@article{arxiv.2308.09961,
title = {The phenomenon of revivals on complex potential Schr\"odinger's equation},
author = {Lyonell Boulton and George Farmakis and Beatrice Pelloni},
journal= {arXiv preprint arXiv:2308.09961},
year = {2024}
}
Comments
17 pages, 2 figures. This paper is published in https://ems.press/journals/zaa/articles/14297854