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.

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.

@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},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2008-2009},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2008-2009____A11_0/}
}
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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://www.numdam.org/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). | MR 2143817 | Zbl 1104.82012

[2] E.H. Lieb, J. Yngvason, The Ground State Energy of a Dilute Two-dimensional Bose Gas, J. Stat. Phys. 103 (2001), 509–526. | MR 1827922 | Zbl 1115.82306

[3] F.J. Dyson, Ground-State Energy of a Hard-Sphere Gas, Phys. Rev. 106 (1957), 20–26. | Zbl 0077.23503

[4] E.H. Lieb, J. Yngvason, Ground State Energy of the Low Density Bose Gas, Phys. Rev. Lett. 80 (1998), 2504–2507. | MR 1886263 | Zbl 1017.82006

[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 2215615

[7] R. Seiringer, Ground State Asymptotics of a Dilute, Rotating Gas, J. Phys. A: Math. Gen. 36 (2003), 9755-9778. | MR 2007281 | Zbl 1151.82401

[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 2395481

[11] M. Correggi, J. Yngvason, Energy and Vorticity in Fast Rotating Bose-Einstein Condensates, arXiv:0806.3191, J.Phys. A 41 (2008), 445002 | MR 2453175 | Zbl 1157.82013