The giant vortex state for a Bose-Einstein condensate in a rotating anharmonic trap: Extreme rotation regimes

Journal des Mathematiques Pures et Appliquees

Volumn 95, Issue 3, 2011, Pages 296-347

  Rougerie, Nicolas ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Bose Einstein condensates; Gross Pitaevskii energy; Vortices

Indexed keywords

EID: 79551641128     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2010.11.004     Document Type: Article

References (44)

1. Aftalion A. Vortices in Bose-Einstein Condensates 2006, Birkhäuser, Boston.
2. Aftalion A., Alama S., Bronsard L. Giant vortex and the breakdown of strong pinning in a rotating Bose-Einstein condensate. Archive for Rational Mechanics and Analysis 2005, 178:247-286.
3. Aftation A., Blanc X. Vortex lattices in rotating Bose-Einstein condensates. SIAM Journal of Mathematical Analysis 2006, 38:874.
4. Aftalion A., Blanc X. Reduced energy functionals for a three dimensional fast rotating Bose-Einstein condensate. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis 2008, 339-355.
5. Aftalion A., Blanc X., Nier F. Lowest Landau Level functionals and Bargmann transform in Bose-Einstein condensates. Journal of Functional Analysis 2006, 241(2):661-702.
6. Aftalion A., Danaila I. Giant vortices in combined harmonic and quartic traps. Physical Review A 2004, 69:033608.
7. Aftalion A., Hellfer B. On mathematical models for Bose-Einstein condensates in optical lattices. Reviews in Mathematical Physics 2009, 21(2):229-278.
8. Bauman P., Phillips D., Tang Q. Stable nucleation for the Ginzburg-Landau system with an applied magnetic field. Archive for Rational Mechanics and Analysis 1998, 142:1-43.
9. Blanc X., Rougerie N. Lowest-Landau-level vortex structure of a Bose-Einstein condensate rotating in a harmonic plus quartic trap. Physical Review A 2008, 77:053615.
10. Béthuel F., Brézis H., Hélein F. Asymptotics for the minimization of a Ginzburg-Landau functional. Calculus of Variations and Partial Differential Equations 1993, 1:123-148.
11. Béthuel F., Brézis H., Hélein F. Ginzburg-Landau Vortices 1994, Birkhäuser, Boston.
12. Bretin V., Stock S., Seurin S., Dalibard J. Fast rotation of a Bose-Einstein condensate. Physical Review Letters 2004, 92:050403.
13. Brézis H. Semilinear equations in RN. Applied Mathematics and Optimization 1984, 12:271-282.
14. Bru J.B., Correggi M., Pickl P., Yngvason J. The TF limit for rapidly rotating Bose gases in anharmonic traps. Communications in Mathematical Physics 2008, 280:517-544.
15. Correggi M., Rindler-Daller T., Yngvason J. Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps. Journal of Mathematical Physics 2007, 48:042104.
16. Correggi M., Rindler-Daller T., Yngvason J. Rapidly rotating Bose-Einstein condensates in homogeneous traps. Journal of Mathematical Physics 2007, 48:102103.
17. Correggi M., Yngvason J. Energy and vorticity in fast rotating Bose-Einstein condensates. Journal of Physics A 2008, 41(44):445002.
18. M. Correggi, N. Rougerie, J. Yngvason, The transition to a giant vortex phase in a fast rotating Bose-Einstein condensate, Communications in Mathematical Physics (2010), in press. arxiv:1005.0686.
19. Danaila I. Three-dimensional vortex structure of a fast rotating Bose-Einstein condensate with harmonic-plus-quarting confinement. Physical Review A 2005, 72:013605.
20. Farina A. From Ginzburg-Landau to Gross-Pitaevskii. Monatshefte für Mathematik 2003, 139:265-269.
21. Fetter A.L. Rotating vortex lattice in a Bose-Einstein condensate trapped in combined quadratic and quartic radial potentials. Physical Review A 2001, 64:063608.
22. Fetter A.L. Rotating trapped Bose-Einstein condensates. Reviews of Modern Physics 2009, 81:647.
23. Fetter A.L., Jackson B., Stringari S. Rapid rotation of a Bose-Einstein condensate in a harmonic plus quartic trap. Physical Review A 2005, 71:013605.
24. Fischer U.R., Baym G. Vortex states of rapidly rotating dilute Bose-Einstein condensates. Physical Review Letters 2003, 90:140402.
25. Fu H., Zaremba E. Transition to the giant vortex state in a harmonic-plus-quartic trap. Physical Review A 2006, 73:013614.
26. Helffer N., Sjöstrand J. Puits multiples en mécanique semi-classique 6. Cas des puits sous-variétés. Annales de l'Institut Henri Poincaré (A) 1987, 46(4):353-372.
27. Ignat R., Millot V. The critical velocity for vortex existence in a two dimensional rotating Bose-Einstein condensate. Journal of Functional Analysis 2006, 260-306.
28. Ignat R., Millot V. Energy expansion and vortex location for a two dimensional rotating Bose-Einstein condensate. Review of Mathematical Physics 2006, 18:119-162.
29. Jackson A.D., Kavoulakis G.M. Vortices and hysteresis in a rotating Bose-Einstein condensate with anharmonic confinement. Physical Review A 2004, 70:023601.
30. Jackson A.D., Kavoulakis G.M., Lundh E. Phase diagram of a rotating Bose-Einstein condensate with anharmonic confinement. Physical Review A 2004, 69:053619.
31. Kasamatsu K., Tsubota M., Ueda M. Giant hole and circular superflow in a fast rotating Bose-Einstein condensate. Physical Review A 2002, 66:050606.
32. Kavoulakis G.M., Baym G. Rapidly rotating Bose-Einstein condensates in anharmonic potentials. New Journal of Physics 2003, 5:51.1.
33. Kim J.K., Fetter A.L. Dynamics of a rapidly rotating Bose-Einstein condensate in a harmonic plus quartic trap. Physical Review A 2005, 72:023619.
34. Lewin M., Seiringer R. Strongly correlated phases in rapidly rotating Bose gases. Journal of Statistical Physics 2009, 137(5-6):1040-1062.
35. Lieb E.H., Loss M. Analysis 1997, American Mathematical Society.
36. Lieb E.H., Seiringer R. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Communications in Mathematical Physics 2005, 103.
37. Lieb E.H., Seiringer R., Solovej J.P., Yngvason J. The Mathematics of the Bose Gas and its Condensation. Oberwolfach Seminar Series 2005, vol. 34. Birkhäuser, Boston.
38. Lu K., Pan X.B. Eigenvalue problems of Ginzburg-Landau operator in bounded domains. Journal of Mathematical Physics 1999, 40:2647-2670.
39. Lundh E. Multiply quantized vortices in trapped Bose-Einstein condensates. Physical Review A 2002, 65:043604.
40. Nirenberg L. On elliptic partial differential equations. Annali Della Scuola Normale Superiore di Pisa 1959, 13:115-162.
41. N. Rougerie, Annular Bose-Einstein condensates in the lowest Landau level, Applied Mathematics Research Express (2010), in press. arxiv:1009.1968.
42. Sandier E., Serfaty S. Vortices in the Magnetic Ginzburg-Landau Model 2007, Birkhäuser, Boston.
43. Seiringer R. Gross-Pitaevskii theory of the rotating Bose gas. Communications in Mathematical Physics 2002, 229:491-509.
44. Bretin V., Stock S., Chevy F., Dalibard J. Shape oscillation of a rotating Bose-Einstein condensate. Europhysics Letters 2004, 65:594.