Reduced energy functionals for a three-dimensional fast rotating Bose Einstein condensates

Aftalion, Amandine; Blanc, Xavier

doi:10.1016/j.anihpc.2006.11.011

Aftalion, Amandine ; Blanc, Xavier

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 2, pp. 339-355

MR | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2006.11.011

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     author = {Aftalion, Amandine and Blanc, Xavier},
     title = {Reduced energy functionals for a three-dimensional fast rotating {Bose} {Einstein} condensates},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {339--355},
     year = {2008},
     publisher = {Elsevier},
     volume = {25},
     number = {2},
     doi = {10.1016/j.anihpc.2006.11.011},
     mrnumber = {2400105},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2006.11.011/}
}

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Aftalion, Amandine; Blanc, Xavier. Reduced energy functionals for a three-dimensional fast rotating Bose Einstein condensates. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 2, pp. 339-355. doi: 10.1016/j.anihpc.2006.11.011

Bibliographie
Cité par

[1] Abo-Shaeer J.R., Raman C., Vogels J.M., Ketterle W., Observation of vortex lattices in Bose-Einstein condensates, Science 292 (2001) 476-479.

[2] Aftalion A., Vortices in Bose Einstein Condensates, Progress in Nonlinear Differential Equations and Their Applications, vol. 67, Birkhäuser, 2006. | Zbl | MR

[3] Aftalion A., Blanc X., Vortex lattices in rotating Bose Einstein condensates, SIAM Math. Anal. 38 (2006) 874. | Zbl | MR

[4] Aftalion A., Blanc X., Dalibard J., Vortex patterns in a fast rotating Bose-Einstein condensate, Phys. Rev. A 71 (2005) 023611.

[5] Aftalion A., Blanc X., Nier F., Lowest Landau level functional and Bargmann transform in Bose Einstein condensates, J. Funct. Anal. 241 (2006) 661. | Zbl | MR

[6] Aftalion A., Jerrard R.L., Properties of a single vortex solution in a rotating Bose Einstein condensate, C. R. Acad. Sci. Paris, Ser. I (2003) 336. | Zbl | MR

[7] Aftalion A., Riviere T., Vortex energy and vortex bending for a rotating Bose-Einstein condensate, Phys. Rev. A 64 (2001) 043611.

[8] Bethuel F., Brezis H., Helein F., Ginzburg-Landau Vortices, Progress in Nonlinear Differential Equations and their Applications, vol. 13, Birkhäuser Boston, Inc., Boston, MA, 1994. | Zbl | MR

[9] Bretin V., Stock S., Seurin Y., Dalibard J., Fast rotation of a Bose-Einstein condensate, Phys. Rev. Lett. 92 (2004) 050403.

[10] Brezis H., Semilinear equations in $R^{N}$ without condition at infinity, Appl. Math. Optim. 12 (1984) 271-282. | Zbl | MR

[11] Coddington I., Haljan P.C., Engels P., Schweikhard V., Tung S., Cornell E.A., Experimental studies of equilibrium vortex properties in a Bose-condensed gas, Phys. Rev. A 70 (2004) 063607.

[12] Cooper N.R., Komineas S., Read N., Vortex lattices in the lowest Landau level for confined Bose-Einstein condensates, Phys. Rev. A 70 (2004) 033604.

[13] Cooper N.R., Wilkin N.K., Gunn J.M.F., Quantum phases of vortices in rotating Bose-Einstein condensates, Phys. Rev. Lett. 87 (2001) 120405.

[14] Engels P. et al. , Observation of long-lived vortex aggregates in rapidly rotating Bose-Einstein condensates, Phys. Rev. Lett. 90 (2003) 170405.

[15] Ho T.L., Bose-Einstein condensates with large number of vortices, Phys. Rev. Lett. 87 (2001) 060403.

[16] Kleiner W.H., Roth L.M., Autler S.H., Bulk solution of Ginzburg-Landau equations for type II superconductors: Upper critical field region, Phys. Rev. 133 (1964) A1226. | Zbl

[17] Lieb E., Loss M., Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, 1997. | Zbl | MR

[18] Lieb E., Seiringer R., Derivation of the Gross-Pitaevskii equation for rotating Bose gases, Comm. Math. Phys. 264 (2006) 505. | MR

[19] Lieb E., Seiringer R., Yngvason J., Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional, Phys. Rev. A 61 (2000) 0436021.

[20] Lu K., Pan X.B., Eigenvalue problem of Ginzburg-Landau operator in bounded domains, J. Math. Phys. 40 (1999) 2647-2670. | Zbl | MR

[21] Madison K., Chevy F., Bretin V., Dalibard J., Vortex formation in a stirred Bose-Einstein condensate, Phys. Rev. Lett. 84 (2000) 806.

[22] Matthews M.R. et al. , Vortices in a Bose-Einstein condensate, Phys. Rev. Lett. 83 (1999) 2498.

[23] Olshanii M., Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81 (1998) 938-941.

[24] Pitaevskii L., Stringari S., Bose-Einstein Condensation, Oxford University Press, Oxford, 2003. | Zbl | MR

[25] Raman C., Abo-Shaeer J.R., Vogels J.M., Xu K., Ketterle W., Vortex nucleation in a stirred Bose-Einstein condensate, Phys. Rev. Lett. 87 (2001) 210402.

[26] Schnee K., Yngvason J., Bosons in disc-shaped traps: From 3D to 2D, preprint, math-ph/0510006. | Zbl | MR

[27] Schweikhard V., Coddington I., Engels P., Mogendorff V.P., Cornell E.A., Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level, Phys. Rev. Lett. 92 (2004) 040404.

[28] Stock S., Bretin V., Chevy F., Dalibard J., Shape oscillation of a rotating Bose-Einstein condensate, Europhys. Lett. 65 (2004) 594.

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