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

top
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

top

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

top
  1. E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason, The Mathematics of the Bose Gas and its Condensation, (Birkhäuser, Basel, 2005). Zbl1104.82012MR2143817
  2. E.H. Lieb, J. Yngvason, The Ground State Energy of a Dilute Two-dimensional Bose Gas, J. Stat. Phys.103 (2001), 509–526. Zbl1115.82306MR1827922
  3. F.J. Dyson, Ground-State Energy of a Hard-Sphere Gas, Phys. Rev.106 (1957), 20–26. Zbl0077.23503
  4. E.H. Lieb, J. Yngvason, Ground State Energy of the Low Density Bose Gas, Phys. Rev. Lett.80 (1998), 2504–2507. Zbl1017.82006MR1886263
  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. Zbl1043.82515
  6. E.H. Lieb, R. Seiringer, Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases, Commun. Math. Phys.264 (2006), 505-537. Zbl1233.82004MR2215615
  7. R. Seiringer, Ground State Asymptotics of a Dilute, Rotating Gas, J. Phys. A: Math. Gen.36 (2003), 9755-9778. Zbl1151.82401MR2007281
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.