On the mean field approximation of many-boson dynamics

Autor: Liard, Quentin

We show under general assumptions that the mean-field approximation for quan- tum many-boson systems is correct. Our contribution unifies and improves on most of the known results. The proof uses general properties of quantization in infinite dimensi

Externí odkaz: http://arxiv.org/abs/1609.06254

Mean field limit for Bosons with compact kernels interactions by Wigner measures transportation

Autor: Pawilowski, Boris, Liard, Quentin

We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the W

Externí odkaz: http://arxiv.org/abs/1402.4261

On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEs

Autor: Ammari, Zied, Liard, Quentin

Publikováno v: Discrete and Continuous Dynamical Systems-Series A
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2018, 38 (2), pp.723-748. ⟨10.3934/dcds.2018032⟩
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2018, 38 (2), pp.723-748. 〈10.3934/dcds.2018032〉
Discrete and Continuous Dynamical Systems-Series A, 2018, 38 (2), pp.723-748. ⟨10.3934/dcds.2018032⟩

In this paper, we give a uniqueness result to a transport equation fulfilled by probability measure on a infinite dimensional Hilbert space. Main arguments are based on projective aspects and a probabilistic representation of the solutions. It extend

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01e60c9d2ec3b490e1fc194a7444d26a
https://hal.archives-ouvertes.fr/hal-01275164v3/document

Dérivation des équations de Schrödinger non linéaires par une méthode des caractéristiques en dimension infinie

Autor: Liard, Quentin

Dans cette thèse, nous aborderons l'approximation de champ moyen pour des particules bosoniques. Pour un certain nombre d'états quantiques, la dérivation de la limite de champ moyen est connue, et il semble naturel d'étendre ces travaux à un cad

Externí odkaz: http://www.theses.fr/2015REN1S126/document

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