# Strong phase-space semiclassical asymptotics

Abstract : Wigner and Husimi transforms have long been used for the phase-space reformulation of Schrödinger-type equations, and the study of the corresponding semiclassical limits. Most of the existing results provide approximations in appropriate weak topologies. In this work we are concerned with semiclassical limits in the strong topology, i.e. approximation of Wigner functions by solutions of the Liouville equation in $L^2$ and Sobolev norms. The results obtained improve the state of the art, and highlight the role of potential regularity, especially through the regularity of the Wigner equation. It must be mentioned that the strong convergence can be shown up to $O(log \frac{1}\epsilon)$ time-scales, which is well known to be, in general, the limit of validity of semiclassical asymptotics.
Type de document :
Article dans une revue
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2011, 43 (5), pp.2116-2149. 〈10.1137/10078712X〉
Domaine :

https://hal.inria.fr/inria-00528984
Contributeur : Agissilaos Athanassoulis <>
Soumis le : samedi 23 octobre 2010 - 16:08:04
Dernière modification le : jeudi 10 mai 2018 - 01:57:23

### Citation

Agissilaos Athanassoulis, Thierry Paul. Strong phase-space semiclassical asymptotics. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2011, 43 (5), pp.2116-2149. 〈10.1137/10078712X〉. 〈inria-00528984〉

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