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Dilute, Trapped Bose Gases and Bose-Einstein Condensation

  • R. Seiringer
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 695)

Abstract

The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases.

Keywords

Ground State Energy Ground State Density Nobel Prize Award Constant Phase Factor Trace Class Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    E.A. Cornell and C.E. Wieman, Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, in: Les Prix Nobel 2001 (The Nobel Foundation, Stockholm, 2002), pp. 87–108. Reprinted in: Rev. Mod. Phys. 74, 875–893 (2002); Chem. Phys. Chem. 3, 476–493 (2002).Google Scholar
  2. 2.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari, Theory of Bose- Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463–512 (1999).CrossRefADSGoogle Scholar
  3. 3.
    F.J. Dyson, Ground-State Energy of a Hard-Sphere Gas, Phys. Rev. 106, 20–26 (1957).zbMATHCrossRefADSGoogle Scholar
  4. 4.
    E.P. Gross, Structure of a Quantized Vortex in Boson Systems, Nuovo Cimento 20, 454–466 (1961). Hydrodynamics of a superfluid condensate, J. Math. Phys. 4, 195–207 (1963).zbMATHCrossRefGoogle Scholar
  5. 5.
    W. Ketterle, When atoms behave as waves: Bose-Einstein condensation and the atom laser, in: Les Prix Nobel 2001 (The Nobel Foundation, Stockholm, 2002), pp. 118–154. Reprinted in: Rev. Mod. Phys. 74, 1131–1151 (2002); Chem. Phys. Chem. 3, 736–753 (2002).Google Scholar
  6. 6.
    W. Lenz, Die Wellenfunktion und Geschwindigkeitsverteilung des entarteten Gases, Z. Phys. 56, 778–789 (1929).zbMATHCrossRefADSGoogle Scholar
  7. 7.
    E.H. Lieb, Simplified Approach to the Ground State Energy of an Imperfect Bose Gas, Phys. Rev. 130, 2518–2528 (1963).CrossRefADSGoogle Scholar
  8. 8.
    E.H. Lieb and W. Liniger, Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Phys.Rev. 130, 1605–1616 (1963). E.H. Lieb, Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum, Phys. Rev. 130, 1616–1624 (1963).zbMATHMathSciNetCrossRefADSGoogle Scholar
  9. 9.
    E.H. Lieb and M. Loss, Analysis, 2nd ed., Amer. Math. Soc., Providence (2001).zbMATHGoogle Scholar
  10. 10.
    E.H. Lieb and R. Seiringer, Proof of Bose-Einstein Condensation for Dilute Trapped Gases, Phys. Rev. Lett. 88, 170409-1–4 (2002).CrossRefADSGoogle Scholar
  11. 11.
    E.H. Lieb, R. Seiringer, J.P. Solovej, and J. Yngvason, The Ground State of the Bose Gas, in: Current Developments in Mathematics, 2001, 131–178, International Press, Cambridge (2002). See also arXiv:math-/0405004Google Scholar
  12. 12.
    E.H. Lieb, R. Seiringer, and J. Yngvason, Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional, Phys. Rev. A 61, 043602-1–13 (2000).CrossRefADSGoogle Scholar
  13. 13.
    E.H. Lieb, R. Seiringer, and J. Yngvason, A Rigorous Derivation of the Gross- Pitaevskii Energy Functional for a Two-Dimensional Bose Gas, Commun. Math. Phys. 224, 17–31 (2001).zbMATHMathSciNetCrossRefADSGoogle Scholar
  14. 14.
    E.H. Lieb, R. Seiringer, and J. Yngvason, Superfluidity in Dilute Trapped Bose Gases, Phys. Rev. B 66, 134529-1–6 (2002).CrossRefADSGoogle Scholar
  15. 15.
    E.H. Lieb, R. Seiringer, and J. Yngvason, Poincaré Inequalities in Punctured Domains, Ann. Math. 158, 1067–1080 (2003).zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    E.H. Lieb, R. Seiringer, and J. Yngvason, One-Dimensional Bosons in Three-Dimensional Traps, Phys. Rev. Lett. 91, 150401-1–4 (2003). One-Dimensional Behavior of Dilute, Trapped Bose Gases, Commun. Math. Phys. 244, 347–393 (2004).CrossRefADSGoogle Scholar
  17. 17.
    E.H. Lieb and J. Yngvason, Ground State Energy of the Low Density Bose Gas, Phys. Rev. Lett. 80, 2504–2507 (1998).CrossRefADSGoogle Scholar
  18. 18.
    E.H. Lieb and J. Yngvason, The Ground State Energy of a Dilute Two- Dimensional Bose Gas, J. Stat. Phys. 103, 509–526 (2001).zbMATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    O. Penrose and L. Onsager, Bose-Einstein Condensation and Liquid Helium, Phys. Rev. 104, 576–584 (1956).zbMATHCrossRefADSGoogle Scholar
  20. 20.
    L.P. Pitaevskii, Vortex lines in an imperfect Bose gas, Sov. Phys. JETP 13, 451–454 (1961).MathSciNetGoogle Scholar
  21. 21.
    M. Reed and B. Simon, Methods of Modern Mathematical Physics IV. Analysis of Operators, Academic Press (1978).Google Scholar
  22. 22.
    R. Seiringer, Gross-Pitaevskii Theory of the Rotating Bose Gas, Commun. Math. Phys. 229, 491–509 (2002).zbMATHMathSciNetCrossRefADSGoogle Scholar
  23. 23.
    R. Seiringer, Ground state asymptotics of a dilute, rotating gas, J. Phys. A: Math. Gen. 36, 9755–9778 (2003).zbMATHMathSciNetCrossRefADSGoogle Scholar
  24. 24.
    B. Simon, Trace ideals and their application, Cambridge University Press (1979).Google Scholar
  25. 25.
    G. Temple, The theory of Rayleigh's principle as applied to continuous systems, Proc. Roy. Soc. London A 119, 276–293 (1928).zbMATHADSCrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • R. Seiringer
    • 1
  1. 1.Department of Physics, Jadwin HallPrinceton UniversityPrincetonUSA

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