[Tourbillons dans un condensat de Bose–Einstein 2d en rotation]
Nous étudions le modèle physique pour un condensat de Bose–Einstein bidimensionnel en rotation. Nous minimisons une fonctionnelle de Gross–Pitaevskii définie sur sous contrainte de masse un. Nous estimons les vitesses critiques pour lesquelles d tourbillons sont présents dans le condensat, puis nous localisons ces tourbillons. Notre méthode est basée sur un développement asymptotique de l'énergie.
We investigate the physical model for a two dimensional rotating Bose–Einstein condensate. We minimize a Gross–Pitaevskii functional defined in under the unit mass constraint. We estimate the critical rotational speeds for having d vortices in the condensate and we determine the location of the vortices. This relies on an asymptotic expansion of the energy.
Publié le :
@article{CRMATH_2005__340_8_571_0,
author = {Ignat, Radu and Millot, Vincent},
title = {Vortices in a 2d rotating {Bose{\textendash}Einstein} condensate},
journal = {Comptes Rendus. Math\'ematique},
pages = {571--576},
publisher = {Elsevier},
volume = {340},
number = {8},
year = {2005},
doi = {10.1016/j.crma.2005.03.015},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.03.015/}
}
TY - JOUR AU - Ignat, Radu AU - Millot, Vincent TI - Vortices in a 2d rotating Bose–Einstein condensate JO - Comptes Rendus. Mathématique PY - 2005 SP - 571 EP - 576 VL - 340 IS - 8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.03.015/ DO - 10.1016/j.crma.2005.03.015 LA - en ID - CRMATH_2005__340_8_571_0 ER -
%0 Journal Article %A Ignat, Radu %A Millot, Vincent %T Vortices in a 2d rotating Bose–Einstein condensate %J Comptes Rendus. Mathématique %D 2005 %P 571-576 %V 340 %N 8 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.03.015/ %R 10.1016/j.crma.2005.03.015 %G en %F CRMATH_2005__340_8_571_0
Ignat, Radu; Millot, Vincent. Vortices in a 2d rotating Bose–Einstein condensate. Comptes Rendus. Mathématique, Tome 340 (2005) no. 8, pp. 571-576. doi : 10.1016/j.crma.2005.03.015. http://archive.numdam.org/articles/10.1016/j.crma.2005.03.015/
[1] Observation of vortex latices in Bose–Einstein condensates, Science, Volume 292 (2001), pp. 476-479
[2] A. Aftalion, S. Alama, L. Bronsard, Giant vortex and the breakdown of strong pinning in a rotating Bose–Einstein condensate, Arch. Rational Mech. Anal., in press
[3] Vortices in a rotating Bose–Einstein condensate: critical angular velocities and energy diagrams in the Thomas–Fermi regime, Phys. Rev. A, Volume 64 (2001), p. 063603
[4] Topological methods for the Ginzburg–Landau equations, J. Math. Pures Appl., Volume 77 (1998), pp. 1-49
[5] Asymptotic behavior of minimizers for the Ginzburg–Landau functional with weight II, Arch. Rational Mech. Anal., Volume 142 (1998), pp. 75-98
[6] Ginzburg–Landau vortices, Progr. Nonlinear Differential Equations Appl., vol. 13, Birkhäuser, 1993
[7] Bose–Einstein condensates with vortices in rotating traps, Eur. Phys. J. D, Volume 7 (1999), pp. 399-412
[8] R. Ignat, V. Millot, The critical velocity for vortex existence in a two dimensional rotating Bose–Einstein condensate, in press
[9] R. Ignat, V. Millot, Energy expansion and vortex location for a two dimensional rotating Bose–Einstein condensate, in press
[10] Ginzburg–Landau type energy with discontinuous constraint, J. Anal. Math., Volume 77 (1999), pp. 1-26
[11] Vortex formation in a stirred Bose–Einstein condensate, Phys. Rev. Lett., Volume 84 (2000), p. 806
[12] Global minimizers for the Ginzburg–Landau functional below the first critical magnetic field, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 17 (2000), pp. 119-145
[13] On a model of rotating superfluids, ESAIM: Control Optim. Calc. Var., Volume 6 (2001), pp. 201-238
Cité par Sources :
