Fast rotating Bose-Einstein condensates and Bargmann transform

Xavier Blanc[1]

  • [1] Université Pierre et Marie Curie (Paris 6), UMR 7598, Laboratoire Jacques-Louis Lions, Paris, F-75005

Séminaire Équations aux dérivées partielles (2005-2006)

  • page 1-18

Abstract

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When a Bose-Einstein condensate (BEC) is rotated sufficiently fast, it nucleates vortices. The system is only stable if the rotational velocity Ω is lower than a critical value Ω c . Experiments show that as Ω approaches Ω c , the condensate nucleates more and more vortices, which become periodically arranged. We present here a mathematical study of this limit. Using Bargmann transform and an analogy with semi-classical analysis in second quantization, we prove that the system necessarily has an infinite number of vortices and provide an ansatz for the solution. This summarizes two joint works, with A. Aftalion (LJLL, Univ. Paris 6) and J. Dalibard (LKB, Ecole Normale Supérieure), on the one hand, and with A. Aftalion and F. Nier (IRMAR, Univ. Rennes I) on the other hand.

How to cite

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Blanc, Xavier. "Fast rotating Bose-Einstein condensates and Bargmann transform." Séminaire Équations aux dérivées partielles (2005-2006): 1-18. <http://eudml.org/doc/11140>.

@article{Blanc2005-2006,
abstract = {When a Bose-Einstein condensate (BEC) is rotated sufficiently fast, it nucleates vortices. The system is only stable if the rotational velocity $\Omega $ is lower than a critical value $\Omega _c$. Experiments show that as $\Omega $ approaches $\Omega _c$, the condensate nucleates more and more vortices, which become periodically arranged. We present here a mathematical study of this limit. Using Bargmann transform and an analogy with semi-classical analysis in second quantization, we prove that the system necessarily has an infinite number of vortices and provide an ansatz for the solution. This summarizes two joint works, with A. Aftalion (LJLL, Univ. Paris 6) and J. Dalibard (LKB, Ecole Normale Supérieure), on the one hand, and with A. Aftalion and F. Nier (IRMAR, Univ. Rennes I) on the other hand.},
affiliation = {Université Pierre et Marie Curie (Paris 6), UMR 7598, Laboratoire Jacques-Louis Lions, Paris, F-75005},
author = {Blanc, Xavier},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-18},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Fast rotating Bose-Einstein condensates and Bargmann transform},
url = {http://eudml.org/doc/11140},
year = {2005-2006},
}

TY - JOUR
AU - Blanc, Xavier
TI - Fast rotating Bose-Einstein condensates and Bargmann transform
JO - Séminaire Équations aux dérivées partielles
PY - 2005-2006
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 18
AB - When a Bose-Einstein condensate (BEC) is rotated sufficiently fast, it nucleates vortices. The system is only stable if the rotational velocity $\Omega $ is lower than a critical value $\Omega _c$. Experiments show that as $\Omega $ approaches $\Omega _c$, the condensate nucleates more and more vortices, which become periodically arranged. We present here a mathematical study of this limit. Using Bargmann transform and an analogy with semi-classical analysis in second quantization, we prove that the system necessarily has an infinite number of vortices and provide an ansatz for the solution. This summarizes two joint works, with A. Aftalion (LJLL, Univ. Paris 6) and J. Dalibard (LKB, Ecole Normale Supérieure), on the one hand, and with A. Aftalion and F. Nier (IRMAR, Univ. Rennes I) on the other hand.
LA - eng
UR - http://eudml.org/doc/11140
ER -

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