Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations

Jakob Yngvason[1]

  • [1] Faculty of Physics University of Vienna Boltzmanngasse 5 1090 Vienna Austria and Erwin Schrödinger Institute for Mathematical Physics Boltzmanngasse 9 1090 Vienna Austria

Séminaire Équations aux dérivées partielles (2008-2009)

  • Volume: 2008-2009, page 1-12

Abstract

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One of the most interesting phenomena exhibited by ultracold quantum gases is the appearance of vortices when the gas is put in rotation. The talk will bring a survey of some recent progress in understanding this phenomenon starting from the many-body ground state of a Bose gas with short range interactions. Mathematically this amounts to describing solutions of a linear Schrödinger equation with a very large number of variables in terms of a nonlinear equation with few variables and analyzing the latter.

How to cite

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Yngvason, Jakob. "Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations." Séminaire Équations aux dérivées partielles 2008-2009 (2008-2009): 1-12. <http://eudml.org/doc/11186>.

@article{Yngvason2008-2009,
abstract = {One of the most interesting phenomena exhibited by ultracold quantum gases is the appearance of vortices when the gas is put in rotation. The talk will bring a survey of some recent progress in understanding this phenomenon starting from the many-body ground state of a Bose gas with short range interactions. Mathematically this amounts to describing solutions of a linear Schrödinger equation with a very large number of variables in terms of a nonlinear equation with few variables and analyzing the latter.},
affiliation = {Faculty of Physics University of Vienna Boltzmanngasse 5 1090 Vienna Austria and Erwin Schrödinger Institute for Mathematical Physics Boltzmanngasse 9 1090 Vienna Austria},
author = {Yngvason, Jakob},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Gross-Pitaevskii equation; Bose-Einstein condensates; many-body problem},
language = {eng},
pages = {1-12},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations},
url = {http://eudml.org/doc/11186},
volume = {2008-2009},
year = {2008-2009},
}

TY - JOUR
AU - Yngvason, Jakob
TI - Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations
JO - Séminaire Équations aux dérivées partielles
PY - 2008-2009
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2008-2009
SP - 1
EP - 12
AB - One of the most interesting phenomena exhibited by ultracold quantum gases is the appearance of vortices when the gas is put in rotation. The talk will bring a survey of some recent progress in understanding this phenomenon starting from the many-body ground state of a Bose gas with short range interactions. Mathematically this amounts to describing solutions of a linear Schrödinger equation with a very large number of variables in terms of a nonlinear equation with few variables and analyzing the latter.
LA - eng
KW - Gross-Pitaevskii equation; Bose-Einstein condensates; many-body problem
UR - http://eudml.org/doc/11186
ER -

References

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  8. E. H. Lieb, R. Seiringer, J. Yngvason, The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime, Phys. Rev. A79 (2009), 063626 
  9. M. Lewin, R. Seiringer, Strongly correlated phases in rapidly rotating Bose gases, arXiv:0906.0741 Zbl1183.82006
  10. J.-B. Bru, M. Correggi, P. Pickl, J. Yngvason, The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps, Commun. Math. Phys.280 (2008), 517-544. Zbl1207.82015MR2395481
  11. M. Correggi, J. Yngvason, Energy and Vorticity in Fast Rotating Bose-Einstein Condensates, arXiv:0806.3191, J.Phys. A41 (2008), 445002 Zbl1157.82013MR2453175

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