[Justification de l'équation de Schrödinger–Poisson à partir du problème quantique à N corps]
On établit la validité de l'équation de Schrödinger–Poisson en régime instationnaire comme limite à couplage faible de l'équation de Schrödinger linéaire à N corps avec potentiel de Coulomb.
We derive the time-dependent Schrödinger–Poisson equation as the weak coupling limit of the N-body linear Schrödinger equation with Coulomb potential.
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@article{CRMATH_2002__334_6_515_0,
author = {Bardos, Claude and Erd\"os, Laszlo and Golse, Fran\c{c}ois and Mauser, Norbert and Yau, Horng-Tzer},
title = {Derivation of the {Schr\"odinger{\textendash}Poisson} equation from the quantum $ \mathbf{N}$-body problem},
journal = {Comptes Rendus. Math\'ematique},
pages = {515--520},
publisher = {Elsevier},
volume = {334},
number = {6},
year = {2002},
doi = {10.1016/S1631-073X(02)02253-7},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02253-7/}
}
TY - JOUR
AU - Bardos, Claude
AU - Erdös, Laszlo
AU - Golse, François
AU - Mauser, Norbert
AU - Yau, Horng-Tzer
TI - Derivation of the Schrödinger–Poisson equation from the quantum $ \mathbf{N}$-body problem
JO - Comptes Rendus. Mathématique
PY - 2002
SP - 515
EP - 520
VL - 334
IS - 6
PB - Elsevier
UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02253-7/
DO - 10.1016/S1631-073X(02)02253-7
LA - en
ID - CRMATH_2002__334_6_515_0
ER -
%0 Journal Article
%A Bardos, Claude
%A Erdös, Laszlo
%A Golse, François
%A Mauser, Norbert
%A Yau, Horng-Tzer
%T Derivation of the Schrödinger–Poisson equation from the quantum $ \mathbf{N}$-body problem
%J Comptes Rendus. Mathématique
%D 2002
%P 515-520
%V 334
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02253-7/
%R 10.1016/S1631-073X(02)02253-7
%G en
%F CRMATH_2002__334_6_515_0
Bardos, Claude; Erdös, Laszlo; Golse, François; Mauser, Norbert; Yau, Horng-Tzer. Derivation of the Schrödinger–Poisson equation from the quantum $ \mathbf{N}$-body problem. Comptes Rendus. Mathématique, Tome 334 (2002) no. 6, pp. 515-520. doi : 10.1016/S1631-073X(02)02253-7. http://www.numdam.org/articles/10.1016/S1631-073X(02)02253-7/
[1] Weak coupling limit of the N-particle Schrödinger equation, Methods Appl. Anal., Volume 7 (2000), pp. 275-293
[2] C. Bardos, F. Golse, A. Gottlieb, N.J. Mauser, On the derivation of nonlinear Schrödinger and Vlasov equations, Proceedings of the I.M.A., Springer-Verlag (to appear)
[3] L. Erdös, H.-T. Yau, Derivation of the nonlinear Schrödinger equation with Coulomb potential, Preprint
[4] The classical limit for quantum mechanical correlation functions, Comm. Math. Phys., Volume 35 (1974), pp. 265-277
[5] The classical field limit of scattering theory for non-relativistic many-boson systems. I and II, Comm. Math. Phys., Volume 66 (1979), pp. 37-76 and 68 (1979) 45–68
[6] On a class of nonlinear Schrödinger equations with nonlocal interactions, Math. Z., Volume 170 (1980), pp. 109-145
[7] Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc., Volume 70 (1951), pp. 195-211
[8] Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., Volume 63 (1934), pp. 183-248
[9] A note on a theorem of Nirenberg, J. Differential Geom., Volume 12 (1977), pp. 629-633
[10] Kinetic equations from hamiltonian dynamics, Rev. Mod. Phys., Volume 52 (1980) no. 3, pp. 569-615
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