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arXiv · 1209.3739

Semi-classical measures for inhomogeneous Schr\"odinger equations on tori

Nicolas Burq
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Abstract

The purpose of this note is to investigate the high frequency behaviour of solutions to linear Schr\"odinger equations. More precisely, Bourgain and Anantharaman-Macia proved that any weak-* limit of the square density of solutions to the time dependent homogeneous Schr\"odinger equation is absolutely continuous with respect to the Lebesgue measure on $R\times T^d$. Our contribution is that the same result automatically holds for non homogeneous Schr\"odinger equations, which allows for abstract potential type perturbations of the Laplace operator.

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Nicolas Burq. 2012-09-17. Semi-classical measures for inhomogeneous Schr\"odinger equations on tori. https://arxiv.org/abs/1209.3739

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