Lowest Landau level functional and Bargmann spaces for Bose-Einstein condensates

Journal of Functional Analysis

Volumn 241, Issue 2, 2006, Pages 661-702

  Aftalion, A ^a   Blanc, X ^a   Nier, F ^b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

Abrikosov lattice; Bargmann spaces; Bargmann transform; Bose Einstein condensates; Pseudo differential calculus; Semi classical analysis; Theta functions

Indexed keywords

EID: 33750205835     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.04.027     Document Type: Article

References (35)

1. Abo-Shaeer J.R., Raman C., Vogels J.M., and Ketterle W. Observation of vortex lattices in Bose-Einstein condensates. Science 292 (2001) 476-479
2. Abrikosov A.A. Magnetic properties of group II superconductors. J. Exp. Theor. Phys. 32 5 (1957) 1147-1182
3. Aftalion A. Vortices in Bose-Einstein Condensates. Progr. Nonlinear Differential Equations Appl. vol. 67 (2006), Birkhäuser, Boston, MA
4. A. Aftalion, X. Blanc, Vortex lattices in rotating Bose-Einstein condensates, SIAM J. Math. Anal., submitted for publication
5. Aftalion A., Blanc X., and Dalibard J. Vortex patterns in fast rotating Bose-Einstein condensates. Phys. Rev. A 71 (2005) 023611
6. Aftalion A., Blanc X., and Nier F. Vortex distribution in the lowest Landau level. Phys. Rev. A 73 (2006) 011601(R)
7. Almog Y. On the bifurcation and stability of periodic solutions of the Ginzburg-Landau equations in the plane. SIAM J. Appl. Math. 61 1 (2000) 149-171
8. Bargmann V. On a Hilbert space of analytic functions and an associated integral transform. Comm. Pure Appl. Math. 14 (1961) 187-214
9. Boas Jr. R.P. Entire Functions (1954), Academic Press, New York
10. Bony J.M., and Chemin J.Y. Espaces fonctionnels associés au calcul de Weyl-Hörmander. Bull. Soc. Math. France 122 1 (1994) 77-118
11. Bony J.M., and Lerner N. Quantification asymptotique et microlocalisation d'ordre supérieur I. Ann. Sci. École Norm. Sup. (4) 22 (1989) 377-433
12. Boutet de Monvel L., and Guillemin V. The Spectral Theory of Toeplitz Operators. Ann. of Math. Stud. vol. 99 (1981), Princeton Univ. Press, Princeton, NJ
13. Carlen E. Some integral identities and inequalities for entire functions and their application to the coherent state transform. J. Funct. Anal. 97 (1991) 231-249
14. Chandrasekharan K. Elliptic Functions. Grundlehren Math. Wiss. vol. 281 (1985), Springer, New York
15. Chemin J.Y. Fluides parfaits incompressibles. Mém. Soc. Math. Fr. (N.S.) 230 (1995)
16. Delort J.M. FBI Transformation. Second Microlocalization and Semilinear Caustics. Lecture Notes in Math. vol. 1522 (1992), Springer, New York
17. Folland G.B. Harmonic Analysis in Phase Space (1989), Princeton Univ. Press, Princeton, NJ
18. Girvin S.M., and Jach T. Formalism for the quantum Hall effect: Hilbert space of analytic functions. Phys. Rev. B 29 (1984) 5617-5625
19. Gross L. Hypercontractivity on complex manifolds. Acta Math. 182 (1999) 159-206
20. Helffer B. Théorie spectrale pour des opérateurs globalement elliptiques. Astérisque 112 (1984)
21. Helffer B., and Nier F. Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians. Lecture Notes in Math. vol. 1862 (2005), Springer, New York
22. Ho T.L. Bose-Einstein condensates with large number of vortices. Phys. Rev. Lett. 87 (2001) 060403
23. Hörmander L. The Analysis of Linear Partial Differential Operators (1985), Springer, Berlin
24. Hörmander L. Lectures on Nonlinear Hyperbolic Differential Equations. Math. Appl. (Berlin) vol. 26 (1997), Springer, Paris
25. Kleiner W.H., Roth L.M., and Autler S.H. Bulk solutions of Ginzburg-Landau equations for type II superconductors: Upper critical field region. Phys. Rev. A 133 5 (1964) 1226-1227
26. Lerner N. The Wick calculus of pseudo-differential operators and energy estimates. New Trends in Microlocal Analysis. Tokyo, 1995 (1997), Springer, Tokyo
27. Martinez A. An Introduction to Semiclassical Analysis and Microlocal Analysis. Universitext (2002), Springer, New York
28. Nelson E. A quartic interaction in two dimensions. Mathematical Theory of Elementary Particles (1966), MIT Press, Cambridge, MA 69-73
29. Nonnenmacher S., and Voros A. Chaotic eigenfunctions in phase space. J. Stat. Phys. 92 (1998) 431-518
30. Robbins H. A remark on Stirling's formula. Amer. Math. Monthly 62 (1955) 26-29
31. Shiffman B., and Zelditch S. Distribution of zeroes of random and quantum chaotic sections of positive line bundles. Comm. Math. Phys. 200 3 (1999) 661-683
32. Sjöstrand J. Singularités analytiques microlocales. Astérisque 95 (1982) 1-166
33. Stock S., Bretin V., Chevy F., and Dalibard J. Shape oscillation of a rotating Bose-Einstein condensate. Europhys. Lett. 65 (2004) 594
34. Törnkvist O. Ginzburg-Landau theory of the electroweak phase transition and analytical results. arXiv:. hep-ph/9204235
35. Watanabe G., Baym G., and Pethick C.J. Landau levels and the Thomas-Fermi structure of rapidly rotating Bose-Einstein condensates. Phys. Rev. Lett. 93 (2004) 190401