Comparison of gapless mean-field theories for trapped Bose-Einstein condensates

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 3, 1998, Pages 2435-2445

  Proukakis, N P ^a,b   Morgan, S A ^b   Choi, S ^b   Burnett, K ^b  

^a INSTITUTE OF ELECTRONIC STRUCTURE AND LASER   (Greece)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000468638     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.2435     Document Type: Article

References (52)

1. D. H. Kobe, Ann. Phys. (N.Y.) 47, 15 (1968); APNYA6
2. G. W. Goble and D. H. Kobe, Phys. Rev. A 10, 851 (1974); PLRAAN
3. D. A. Huse and E. D. Siggia, Low Temp. Phys. 46, 137 (1982) and references therein.LTPHEG
4. M. Girardeau and R. Arnowitt, Phys. Rev. 113, 755 (1959); PHRVAO
5. Phys. Rev.G. Wentzel, 120, 1572 (1960);
6. P. C. Hohenberg and P. C. Martin, Ann. Phys. (N.Y.) 34, 291 (1965).APNYA6
7. J. P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1986).
8. H. T. C. Stoof, Phys. Rev. A 49, 3824 (1994).PLRAAN
9. J. Goldstone, Nuovo Cimento 19, 154 (1961).NUCIAD
10. V. N. Popov, Functional Integrals and Collective Modes (Cambridge University Press, New York, 1987), Chap. 6.
11. H. Shi, G. Verechaka, and A. Griffin, Phys. Rev. B 50, 1119 (1994).PRBMDO
12. A. Griffin, Phys. Rev. B 53, 9341 (1996).PRBMDO
13. D. A. W. Hutchinson, E. Zaremba, and A. Griffin, Phys. Rev. Lett. 78, 1842 (1997).PRLTAO
14. R. J. Dodd, M. Edwards, C. W. Clark, and K. Burnett, Phys. Rev. A 57, 32 (1998).PLRAAN
15. S. Giorgini, L. P. Pitaevskii, and S. Stringari, J. Low Temp. Phys. 109, 309 (1997).JLTPAC
16. D. S. Jin, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 78, 764 (1997).PRLTAO
17. H. Shi, Ph.D. thesis, Univerity of Toronto, 1997 (unpublished);H. Shi and A. Griffin, Phys. Rep. (to be published).
18. N. P. Proukakis, K. Burnett, and H. T. C. Stoof, Phys. Rev. A 57, 1230 (1998).PLRAAN
19. A. Minguzzi and M. P. Tosi, J. Phys: Condens. Matter 9, 10 211 (1997).JCOMEL
20. S. Giorgini, e-print cond-mat/9709259.
21. E. Zaremba, A. Griffin, and T. Nikuni, e-print cond-mat/9705134.
22. K. Huang and C. N. Yang, Phys. Rev. 106, 1135 (1957); PHRVAO
23. K. Huang, Statistical Mechanics, 2nd ed. (Wiley, New York, 1987).
24. For a nontechnical account, see N. P. Proukakis and K. Burnett, Philos. Trans. R. Soc. London, Ser. A 355, 2235 (1997).PTRMAD
25. For the experimental techniques used in determining the scattering length, see, e.g., E. Tiesinga, C. J. Williams, P. S. Julienne, K. M. Jones, P. D. Lett, and W. D. Phillips, J. Res. Natl. Inst. Stand. Technol. 101, 505 (1996).JRITEF
26. E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics Landau and Lifshitz Course of Theoretical Physics Vol. 9 (Pergamon, Oxford, 1980), Pt. 2.
27. H. T. C. Stoof, M. Bijlsma, and M. Houbiers, J. Res. Natl. Inst. Stand. Technol. 101, 443 (1996).JRITEF
28. M. Bijlsma and H. T. C. Stoof, Phys. Rev. A 55, 498 (1997).PLRAAN
29. See, e.g., F. Takano, Phys. Rev. 123, 699 (1961); PHRVAO
30. A. Coniglio and M. Marinaro, Nuovo Cimento 48, 262 (1967).NUCIAD
31. A. L. Fetter, Ann. Phys. (N.Y.) 70, 67 (1972).APNYA6
32. H. T. C. Stoof (private communication).
33. The full HFB theory cannot be written in the form of Eqs. (1234), because to obtain the full HFB theory from them, one would have to (i) set (Formula presented) throughout Eqs. (1234), (ii) set (Formula presented) in both the time-independent NLSE [Eq. (1)] and the off-diagonal terms mixing (Formula presented) and (Formula presented) in Eqs. (2) and (3), and simultaneously (iii) replace (Formula presented) in the operator (Formula presented) [Eq. (4)] appearing in Eqs. (2) and (3). This last step implies that the full HFB theory cannot be recovered from Eqs. (1234) with a singly defined condensate-condensate interaction (Formula presented) and this leads to the appearance of a gap in the spectrum of elementary excitations.
34. N. P. Proukakis and K. Burnett, J. Res. Natl. Inst. Stand. Technol. 101, 457 (1996).JRITEF
35. N. P. Proukakis, Ph.D. thesis, University of Oxford, 1997 (unpublished).
36. N. N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947).JOPYA6
37. A. A. Abrikosov, L. P. Gor‘kov, and I. E. Dzyaloshinskiĭ, Quantum Field Theoretical Methods in Statistical Physics (Pergamon, Oxford, 1965).
38. F. Mohling and A. Sirlin, Phys. Rev. 118, 370 (1960).PHRVAO
39. W. Ketterle and N. J. van Druten, Phys. Rev. A 54, 656 (1996).PLRAAN
40. M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, Phys. Rev. Lett. 77, 988 (1996).PRLTAO
41. S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 78, 3987 (1997).PRLTAO
42. Although mean-field effects reduce the atomic density at the center of the trap (in the case of repulsive interactions), thus moving the system away from the critical region, the required central density for Bose condensation is simultaneously reduced due to the competing fluctuation effects 38. Nonetheless, such effects do not fully compensate for the increase in the critical number of particles predicted by mean-field theory [
43. M. Houbiers, H. T. C. Stoof, and E. A. Cornell, Phys. Rev. A 56, 2041 (1997)].PLRAAN
44. The definition of a “pseudocritical” temperature in one dimension is further discussed in W. J. Mullin, J. Low Temp. Phys. 106, 615 (1997); JLTPAC
45. S. Grossmann and M. Holthaus, Phys. Rev. E 54, 3495 (1996).PLEEE8
46. M. Bijlsma and H. T. C. Stoof, Phys. Rev. A 54, 5085 (1996).PLRAAN
47. Y. A. Nepomnyashchii and A. A. Nepomnyashchii, Zh. Eksp. Teor. Fiz. 75, 976 (1978) [Sov. Phys. JETP 48, 493 (1979)].SPHJAR
48. See standard textbooks like J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, London, 1989).
49. See J. F. Dobson, Phys. Rev. Lett. 73, 2244 (1994), and references therein.PRLTAO
50. E. Zaremba (private communication).
51. R. J. Dodd (private communication).
52. P. Nozieres and P. Pines, The Theory of Quantum Liquids (Addison-Wesley, Reading, MA, 1990), Vol. II.