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Damping of phase fluctuations in superfluid Bose gases

  • P. LangeEmail author
  • P. Kopietz
  • A. Kreisel
Regular Article

Abstract.

Using Popov’s hydrodynamic approach we derive an effective Euclidean action for the long-wavelength phase fluctuations of superfluid Bose gases in D dimensions. We then use this action to calculate the damping of phase fluctuations at zero temperature as a function of D. For D > 1 and wavevectors |k| ≪ 2mc (where m is the mass of the bosons and c is the sound velocity) we find that the damping in units of the phonon energy E k  = c|k| is to leading order γ k /E k = A D(k 0 D /2πρ)(|k|/k0)2D-2, where ρ is the boson density and k 0 = 2mc is the inverse healing length. For D → 1 the numerical coefficient A D vanishes and the damping is proportional to an additional power of |k|/k 0; a self-consistent calculation yields in this case γ k /E k  = 1.32 (k 0/2πρ)1/2|k|/k 0. In one dimension, we also calculate the entire spectral function of phase fluctuations.

Keywords

Solid State and Materials 

References

  1. 1.
    S.T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 417 (1958)Google Scholar
  2. 2.
    S.T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 433 (1958)[Sov. Phys. JETP 7, 289 (1958); Sov. Phys. JETP 7, 299 (1958)]Google Scholar
  3. 3.
    J. Gavoret, P. Nozières, Ann. Phys. 28, 349 (1964)ADSCrossRefGoogle Scholar
  4. 4.
    H. Shi, A. Griffin, Phys. Rep. 304, 1 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    J.O. Andersen, Rev. Mod. Phys. 76, 599 (2004)ADSzbMATHCrossRefGoogle Scholar
  6. 6.
    N.N. Bogoliubov, Izv. Akad. Nauk SSSR, Ser. Fiz. 11, 77 (1947) [J. Phys. (Moscow) 11, 23 (1947)]Google Scholar
  7. 7.
    A.A. Nepomnyashchy, Yu.A. Nepomnyashchy, Pis’ma Zh. Eksp. Teor. Fiz. 21, 3 (1975) [JETP Lett. 21, 1 (1975)]Google Scholar
  8. 8.
    A.A. Nepomnyashchy, Yu.A. Nepomnyashchy, Zh. Eksp. Teor. Fiz. 75, 976 (1978) [Sov. Phys. JETP 48, 493 (1978)]Google Scholar
  9. 9.
    Yu.A. Nepomnyashchy, Zh. Eksp. Teor. Fiz. 85, 1244 (1983) [Sov. Phys. JETP 58, 722 (1983)]Google Scholar
  10. 10.
    N. Dupuis, Phys. Rev. E 83, 031120 (2011)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    C. Castellani, C. Di Castro, F. Pistolesi, G.C. Strinati, Phys. Rev. Lett. 78, 1612 (1997)ADSCrossRefGoogle Scholar
  12. 12.
    F. Pistolesi, C. Castellani, C. Di Castro, G.C. Strinati, Phys. Rev. B 69, 024513 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    A. Sinner, N. Hasselmann, P. Kopietz, Phys. Rev. Lett. 102, 120601 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    A. Sinner, N. Hasselmann, P. Kopietz, Phys. Rev. A 82, 063632 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    N. Dupuis, Phys. Rev. Lett. 102, 190401 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    N. Dupuis, Phys. Rev. A 80, 043627 (2009)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    V.N. Popov, Teor. Mat. Fiz. 11, 354 (1972) [Theor. Math. Phys. 11, 565 (1972)]Google Scholar
  18. 18.
    V.N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics (Kluwer, Dordrecht, 1983)Google Scholar
  19. 19.
    V.N. Popov, Teor. Mat. Fiz. 30, 346 (1977) [Theor. Math. Phys. 30, 222 (1977)]CrossRefGoogle Scholar
  20. 20.
    E.H. Lieb, W. Liniger, Phys. Rev. 130, 1605 (1963)MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 21.
    E.H. Lieb, Phys. Rev. 130, 1616 (1963)MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    M. Khodas, M. Pustilnik, A. Kamenev, L.I. Glazman, Phys. Rev. Lett. 99, 110405 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    A. Imambekov, L.I. Glazman, Phys. Rev. Lett. 100, 206805 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    A. Kreisel, F. Sauli, N. Hasselmann, P. Kopietz, Phys. Rev. B 78, 035127 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    M. Olshanii, Phys. Rev. Lett. 81, 938 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    M.-C. Chung, A. Bhattacherjee, New J. Phys. 11, 123012 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    M.E. Zhitomirsky, A.L. Chernyshev, arXiv:1205.5278v2 [cond-mat.str-el] (2012)Google Scholar
  28. 28.
    K.V. Samokhin, J. Phys.: Condens. Matter 10, L533 (1998)ADSCrossRefGoogle Scholar
  29. 29.
    M. Pustilnik, M. Khodas, A. Kamenev, L.I. Glazman, Phys. Rev. Lett. 96, 196405 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    A.F. Andreev, Zh. Eksp. Teor. Fiz. 78, 2064 (1980) [Sov. Phys. JETP 51, 1038 (1980)]ADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut für Theoretische Physik, Universität FrankfurtFrankfurtGermany
  2. 2.Department of PhysicsUniversity of FloridaGainesvilleUSA

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