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| HAL : hal-00462536, version 2 |
| DOI : 10.1016/j.matpur.2010.12.004 |
| Fiche détaillée |  Récupérer au format |
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| Journal de mathématiques pures et appliquées 95, 6 (2011) 585-626 |
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| Versions disponibles : | v1 (10-03-2010) | v2 (09-05-2010) |
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| Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states |
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| Zied Ammari 1Francis Nier 1 |
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| (2011) |
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| Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the Wick calculus defined for polynomials are preserved by the action of a nonlinear flow. Nevertheless taking advantage carefully of the information brought by these two calculuses in the mean field asymptotics, the propagation of Wigner measures for general states can be proved, extending to the infinite dimensional case a standard result of semiclassical analysis. |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II |
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| Equations aux dérivées partielles |
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| Domaine | : | Mathématiques/Physique mathématique Physique/Physique mathématique |
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| Mean field – Semiclassical – Wigner measure – BBGKY hierarchy – Second quantization – Fock space |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00462536, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00462536 | |
| oai:hal.archives-ouvertes.fr:hal-00462536 | |
| Contributeur : Zied Ammari | |
| Soumis le : Samedi 8 Mai 2010, 11:33:21 | |
| Dernière modification le : Vendredi 24 Juin 2011, 11:38:00 | |
