On well-posedness and uniqueness for general hierarchy equations of Gross-Pitaevskii and Hartree type

Autor: Ammari, Zied, Liard, Quentin, Rouffort, Clément

Gross-Pitaevskii and Hartree hierarchies are infinite systems of coupled PDEs emerging naturally from the mean field theory of Bose gases. Their solutions are known to be related to an initial value problem, respectively the Gross-Pitaevskii and Hart

Externí odkaz: http://arxiv.org/abs/1802.09041

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

Derivation of the non linear Schrödinger equations by the characteristics method in a infinite dimensional space

Autor: Liard , Quentin

Publikováno v: Equations aux dérivées partielles [math.AP]. Université Rennes 1, 2015. Français. ⟨NNT : 2015REN1S126⟩
Equations aux dérivées partielles [math.AP]. Université Rennes 1, 2015. Français. 〈NNT : 2015REN1S126〉
Equations aux dérivées partielles [math.AP]. Université de Rennes, 2015. Français. ⟨NNT : 2015REN1S126⟩

In this thesis, we justify the mean field approximation in a general framework for bosonic systems. The derivation of mean field dynamics is known for some specific quantum states. Therefore it is natural to expect the extension of these results for

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::48fc2dae8bd347018383d523125582de
https://tel.archives-ouvertes.fr/tel-01269730v2/document