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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.
Yngvason, Jakob 1
@article{SEDP_2008-2009____A11_0,
author = {Yngvason, Jakob},
title = {Bosons in {Rapid} {Rotation:} {From} the {Quantum} {Many-Body} {Problem} to {Effective} {Equations}},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:11},
pages = {1--12},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2008-2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEDP_2008-2009____A11_0/}
}
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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:11 PY - 2008-2009 SP - 1 EP - 12 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://geodesic.mathdoc.fr/item/SEDP_2008-2009____A11_0/ LA - en ID - SEDP_2008-2009____A11_0 ER -
%0 Journal Article %A Yngvason, Jakob %T Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:11 %D 2008-2009 %P 1-12 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://geodesic.mathdoc.fr/item/SEDP_2008-2009____A11_0/ %G en %F SEDP_2008-2009____A11_0
Yngvason, Jakob. Bosons in Rapid Rotation: From the Quantum Many-Body Problem to Effective Equations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2008-2009), Exposé no. 11, 12 p. http://geodesic.mathdoc.fr/item/SEDP_2008-2009____A11_0/
[1] E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason, The Mathematics of the Bose Gas and its Condensation, (Birkhäuser, Basel, 2005). | Zbl | MR
[2] E.H. Lieb, J. Yngvason, The Ground State Energy of a Dilute Two-dimensional Bose Gas, J. Stat. Phys. 103 (2001), 509–526. | Zbl | MR
[3] F.J. Dyson, Ground-State Energy of a Hard-Sphere Gas, Phys. Rev. 106 (1957), 20–26. | Zbl
[4] E.H. Lieb, J. Yngvason, Ground State Energy of the Low Density Bose Gas, Phys. Rev. Lett. 80 (1998), 2504–2507. | Zbl | MR
[5] E.H. Lieb, R. Seiringer, J. Yngvason, Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional, Phys. Rev. A 61 (2000), 043602.
[6] E.H. Lieb, R. Seiringer, Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases, Commun. Math. Phys. 264 (2006), 505-537. | MR
[7] R. Seiringer, Ground State Asymptotics of a Dilute, Rotating Gas, J. Phys. A: Math. Gen. 36 (2003), 9755-9778. | Zbl | MR
[8] E. H. Lieb, R. Seiringer, J. Yngvason, The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime, Phys. Rev. A 79 (2009), 063626
[9] M. Lewin, R. Seiringer, Strongly correlated phases in rapidly rotating Bose gases, arXiv:0906.0741
[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. | MR
[11] M. Correggi, J. Yngvason, Energy and Vorticity in Fast Rotating Bose-Einstein Condensates, arXiv:0806.3191, J.Phys. A 41 (2008), 445002 | Zbl | MR