Applied Physics B

, Volume 117, Issue 3, pp 775–784 | Cite as

A grand-canonical approach to the disordered Bose gas

  • Christopher Gaul
  • Cord A. Müller


We study the problem of disordered interacting bosons within grand-canonical thermodynamics and Bogoliubov theory. We compute the fractions of condensed and non-condensed particles and corrections to the compressibility and the speed of sound due to interaction and disorder. There are two small parameters, the disorder strength compared to the chemical potential and the dilute-gas parameter.


External Potential Quantum Fluctuation Disorder Strength Condensate Fraction Condensate Density 
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.


  1. 1.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  2. 2.
    C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2002)Google Scholar
  3. 3.
    L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003)zbMATHGoogle Scholar
  4. 4.
    B. Nikolić, A. Balaž, A. Pelster, Phys. Rev. A 88, 013624 (2013)Google Scholar
  5. 5.
    C. Gaul, C.A. Müller, Phys. Rev. A. 83, 063629 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    C.A. Müller, C. Gaul, New J. Phys. 14, 075025 (2012)CrossRefGoogle Scholar
  7. 7.
    S. Krinner, D. Stadler, J. Meineke, J.-P. Brantut, T. Esslinger, Phys. Rev. Lett. 110, 100601 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    T.D. Lee, K. Huang, C.N. Yang, Phys. Rev. 106, 1135–1145 (1957)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    O. Penrose, L. Onsager, Phys. Rev. 104, 576–584 (1956)ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    C. Gaul, C.A. Müller, Eur. Phys. J. Special Top. 217, 69–78 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    N.M. Hugenholtz, D. Pines, Phys. Rev. 116, 489–506 (1959)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    A.J. Leggett, Rev. Mod. Phys. 73, 307–356 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    M. Ueda, Fundamentals and New Frontiers of Bose-Einstein Condensation (World Scientific, Singapore, 2010)CrossRefzbMATHGoogle Scholar
  14. 14.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)Google Scholar
  15. 15.
    S. Ronen, J. Phys. B At. Mol. Opt. Phys. 42, 055301 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    D. Guéry-Odelin, T. Lahaye et al., in Les Houches Session XCI, Ultracold Gases and Quantum Information, ed. by C. Miniatura (Oxford University Press, Oxford, 2011)Google Scholar
  17. 17.
    G.E. Astrakharchik, K.V. Krutitsky, Phys. Rev. A 84, 031604 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    V.I. Yukalov, R. Graham, Phys. Rev. A 75, 023619 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    L. Sanchez-Palencia, Phys. Rev. A 74, 053625 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    C. Gaul, Bogoliubov Excitations of Inhomogeneous Bose-Einstein Condensates, Ph.D. thesis, Universität Bayreuth (2010)Google Scholar
  21. 21.
    G.M. Falco, A. Pelster, R. Graham, Phys. Rev. A 75, 063619 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    A.L. Fetter, Ann. Phys. 70, 67–101 (1972)ADSCrossRefGoogle Scholar
  23. 23.
    C. Mora, Y. Castin, Phys. Rev. A 67, 053615 (2003)ADSCrossRefGoogle Scholar
  24. 24.
    J. Saliba, P. Lugan, V. Savona, New J. Phys. 15, 045006 (2013)Google Scholar
  25. 25.
    C. Gaul, J. Schiefele, J. Phys. A Math. Theor. 47, 025002 (2014)ADSCrossRefMathSciNetGoogle Scholar
  26. 26.
    H. Bruus, K. Flensberg, Many-Body Quantum Theory in Condensed Matter Physics (Oxford University Press, Oxford, 2004)Google Scholar
  27. 27.
    K. Huang, H.-F. Meng, Phys. Rev. Lett. 69, 644–647 (1992)ADSCrossRefGoogle Scholar
  28. 28.
    M. Kobayashi, M. Tsubota, Phys. Rev. B 66, 174516 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    A.V. Lopatin, V.M. Vinokur, Phys. Rev. Lett. 88, 235503 (2002)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Max Planck Institute for the Physics of Complex SystemsDresdenGermany
  2. 2.Fachbereich PhysikUniversität KonstanzKonstanzGermany
  3. 3.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore

Personalised recommendations