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arXiv · 1211.1518

Long-time dynamics of completely integrable Schrödinger flows on the torus

Nalini Anantharaman·Clotilde Fermanian-Kammerer·Fabricio Macià
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Abstract

In this article, we are concerned with long-time behaviour of solutions to a semi-classical Schrödinger-type equation on the torus. We consider time scales which go to infinity when the semi-classical parameter goes to zero and we associate with each time-scale the set of semi-classical measures associated with all possible choices of initial data. We emphasize the existence of a threshold: for time-scales below this threshold, the set of semi-classical measures contains measures which are singular with respect to Lebesgue measure in the "position" variable, while at (and beyond) the threshold, all the semi-classical measures are absolutely continuous in the "position" variable.

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Nalini Anantharaman, Clotilde Fermanian-Kammerer, Fabricio Macià. 2012-11-07. Long-time dynamics of completely integrable Schrödinger flows on the torus. https://arxiv.org/abs/1211.1518

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