Laser Physics

, Volume 19, Issue 4, pp 571–577

Effect of random on-site energies on the critical temperature of a lattice Bose gas

  • L. Dell’Anna
  • S. Fantoni
  • P. Sodano
  • A. Trombettoni
Physics of Cold Trapped Atoms

Abstract

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance ν02. By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for ν02 ≪ 1, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.

PACS numbers

40 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. W. Anderson, Phys. Rev. 109, 1492 (1958).CrossRefADSGoogle Scholar
  2. 2.
    T. V. Ramakrishnan, in Chance and Matter, Ed. by J. Souletie, J. Vannimenus, and R. Stora, Les Houches, Session XLVI (North-Holland, Amsterdam, 1987), p. 213.Google Scholar
  3. 3.
    C. W. Kiewiet, H. E. Hall, and J. D. Reppy, Phys. Rev. Lett. 35, 1286 (1975).CrossRefADSGoogle Scholar
  4. 4.
    J. A. Hertz, L. Fleishman, and P. W. Anderson, Phys. Rev. Lett. 43, 942 (1979).CrossRefADSGoogle Scholar
  5. 5.
    M. P. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).CrossRefADSGoogle Scholar
  6. 6.
    K. Huang and H.-F. Meng, Phys. Rev. Lett. 69, 644 (1992)CrossRefADSGoogle Scholar
  7. 7.
    S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. B 49, 12938 (1994).Google Scholar
  8. 8.
    C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Alkali Gases (Cambridge Univ., Cambridge, 2002).Google Scholar
  9. 9.
    L. P. Pitaveskii and S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003).Google Scholar
  10. 10.
    J. E. Lye, L. Fallani, M. Modugno, D. S. Wiersma, C. Fort, and M. Inguscio, Phys. Rev. Lett. 95, 070401 (2005).Google Scholar
  11. 11.
    D. Clement, A. F. Varon, M. Hugbart, J. A. Retter, P. Bouyer, L. Sanchez-Palencia, D. M. Gangardt, G. V. Shlyapnikov, and A. Aspect, Phys. Rev. Lett. 95, 170409 (2005).Google Scholar
  12. 12.
    L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Phys. Rev. Lett. 98, 130404 (2007).Google Scholar
  13. 13.
    G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Nature 453, 895 (2008).CrossRefADSGoogle Scholar
  14. 14.
    J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).CrossRefADSGoogle Scholar
  15. 15.
    O. Morsch and M. Oberthaler, Rev. Mod. Phys. 78, 179 (2006).CrossRefADSGoogle Scholar
  16. 16.
    D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).CrossRefADSGoogle Scholar
  17. 17.
    T. Giamarchi and H. J. Schulz, Phys. Rev. B 37, 325 (1988).CrossRefADSGoogle Scholar
  18. 18.
    H. Gimperlein, S. Wessel, J. Schmiedmayer, and L. Santos, Phys. Rev. Lett. 95, 170401 (2005).Google Scholar
  19. 19.
    A. M. Rey, I. I. Satija, and C. W. Clark, Phys. Rev. A 73, 063610 (2006).Google Scholar
  20. 20.
    K. V. Krutitsky, A. Pelster, and R. Graham, New J. Phys. 8, 187 (2006).CrossRefADSGoogle Scholar
  21. 21.
    T. Roscilde and J. I. Cirac, Phys. Rev. Lett. 98, 190402 (2007).Google Scholar
  22. 22.
    P. Sengupta and S. Haas, Phys. Rev. Lett. 99, 050403 (2007).Google Scholar
  23. 23.
    P. Buonsante, V. Penna, A. Vezzani, and P. B. Blakie, Phys. Rev. A 76, 011602 (2007).Google Scholar
  24. 24.
    T. Roscilde, Phys. Rev. A 77, 063605 (2008).Google Scholar
  25. 25.
    X. Deng, R. Citro, A. Minguzzi, and E. Orignac, Phys. Rev. A 78, 013625 (2008).Google Scholar
  26. 26.
    G. Roux, T. Barthel, I. P. McCulloch, C. Kollath, U. Schollwöck, and T. Giamarchi, Phys. Rev. A 78, 023628 (2008).Google Scholar
  27. 27.
    S. Morrison, A. Kantian, A. J. Daley, H. G. Katzgraber, M. Lewenstein, H. P. Buchler, and P. Zoller, New J. Phys. 10, 073032 (2008).Google Scholar
  28. 28.
    K. V. Krutitsky, M. Thorwart, R. Egger, and R. Graham, Phys. Rev. A 77, 053609 (2008).Google Scholar
  29. 29.
    U. Bissbort and W. Hofstetter, arXiv:0804.0007.Google Scholar
  30. 30.
    G. Roati, M. Zaccanti, C. D’Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, Phys. Rev. Lett. 99, 010403 (2007).Google Scholar
  31. 31.
    L. Dell’Anna, S. Fantoni, P. Sodano, and A. Trombettoni, J. Stat. Mech. P11012 (2008).Google Scholar
  32. 32.
    A. V. Lopatin and V. M. Vinokur, Phys. Rev. Lett. 88, 235503 (2002).Google Scholar
  33. 33.
    O. Zobay, Phys. Rev. A 73, 023616 (2006).Google Scholar
  34. 34.
    M. Timmer, A. Pelster, and R. Graham, Europhys. Lett. 76, 760 (2006).CrossRefADSGoogle Scholar
  35. 35.
    G. M. Falco, A. Pelster, and R. Graham, Phys. Rev. A 75, 063619 (2007).Google Scholar
  36. 36.
    V. I. Yukalov and R. Graham, Phys. Rev. A 75, 023619 (2007).Google Scholar
  37. 37.
    V. I. Yukalov, E. P. Yukalova, K. V. Krutitsky, and R. Graham, Phys. Rev. A 76, 053623 (2007).Google Scholar
  38. 38.
    D. C. Mattis, The Theory of Magnetism II (Springer, Berlin, 1985).Google Scholar
  39. 39.
    L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).MATHGoogle Scholar
  40. 40.
    C. De Dominicis and I. Giardina, Random Fields and Spin Glasses: A Field Theory Approach (Cambridge Univ., Cambridge, 2006).MATHGoogle Scholar
  41. 41.
    G. S. Joyce, J. Phys. A 5, L65 (1972).CrossRefADSGoogle Scholar
  42. 42.
    Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Ed. by M. Abramowitz and I. A. Stegun (National Bureau of Standards, Washington, DC, 1964).MATHGoogle Scholar
  43. 43.
    J.-P. Blaizot, arXiv:0801.0009.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • L. Dell’Anna
    • 1
  • S. Fantoni
    • 1
    • 2
    • 3
  • P. Sodano
    • 4
  • A. Trombettoni
    • 1
    • 2
  1. 1.International School for Advanced StudiesTriesteItaly
  2. 2.INFNSezione di TriesteTriesteItaly
  3. 3.INFMCNR-DEMOCRITOS National Supercomputing CenterTriesteItaly
  4. 4.Dipartimento di Fisica and INFN, Sezione di PerugiaUniversità di PerugiaPerugiaItaly

Personalised recommendations