Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 1, 2000, Pages 136021-1360210

  Guilleumas, M ^a   Pitaevskii, L P ^a,b  

^a UNIVERSITY OF TRENTO   (Italy)

^b KAPITZA INSTITUTE FOR PHYSICAL PROBLEMS   (Russian Federation)

Author keywords

[No Author keywords available]

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EID: 0009311369     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. D.S. Jin, M.R. Matthews, J.R. Ensher, C.E. Wieman, and E.A. Cornell, Phys. Rev. Lett. 78, 764 (1997).
2. 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).
3. W.V. Liu and W.C. Schieve, e-print cond-mat/9702122.
4. L.P. Pitaevskii and S. Stringari, Phys. Lett. A 235, 398 (1997).
5. W.V. Liu, Phys. Rev. Lett. 79, 4056 (1997).
6. S. Giorgini, Phys. Rev. A 57, 2949 (1998).
7. P.O. Fedichev, G.V. Shlyapnikov, and J.T.M. Walraven, Phys. Rev. Lett. 80, 2269 (1998).
8. P.O. Fedichev and G.V. Shlyapnikov, Phys. Rev. A 58, 3146 (1998).
9. N.N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947).
10. E.P. Gross, Nuovo Cimento 20, 454 (1961); E.P. Gross, J. Math. Phys. 4, 195 (1963).
11. E.P. Gross, Nuovo Cimento 20, 454 (1961); E.P. Gross, J. Math. Phys. 4, 195 (1963).
12. L.P. Pitaevskii, Zh. Éksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
13. L.P. Pitaevskii, Zh. Éksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
14. W. Ketterle, D.S. Durfee, and D.M. Stamper-Kurn, e-print cond-mat/9904034.
15. M. Edwards, P.A. Ruprecht, K. Burnett, R.J. Dodd, and C.W. Clark, Phys. Rev. Lett. 77, 1671 (1996);
16. P.A. Ruprecht, M. Edwards, K. Burnett, and C.W. Clark, Phys. Rev. A 54, 4178 (1996); M. Edwards, R.J. Dodd, C.W. Clark, and K. Burnett, J. Res. Natl. Inst. Stand. Technol. 101, 553 (1996).
17. P.A. Ruprecht, M. Edwards, K. Burnett, and C.W. Clark, Phys. Rev. A 54, 4178 (1996); M. Edwards, R.J. Dodd, C.W. Clark, and K. Burnett, J. Res. Natl. Inst. Stand. Technol. 101, 553 (1996).
18. K.G. Singh and D.S. Rokhsar, Phys. Rev. Lett. 77, 1667 (1996).
19. B.D. Esry, Phys. Rev. A 55, 1147 (1997).
20. D.A.W. Hutchinson, E. Zaremba, and A. Griffin, Phys. Rev. Lett. 78, 1842 (1997).
21. L. You, W. Hoston, and M. Lewenstein, Phys. Rev. A 55, R1581 (1997).
22. F. Dalfovo, S. Giorgini, M. Guilleumas, L.P. Pitaevskii, and S. Stringari, Phys. Rev. A 56, 3840 (1997).
23. S. Stringari, Phys. Rev. Lett. 77, 2360 (1996).
24. M is very small.
25. Beliaev decay of an elementary excitation into a pair of excitations (S.T. Beliaev, Zh. Éksp. Teor. Fiz. 7, 469 1958) [Sov. Phys. JETP 34, 322 (1958)] is not active for the lowest-energy modes in the case of the trapping potential because of the discretization of levels.
26. Beliaev decay of an elementary excitation into a pair of excitations (S.T. Beliaev, Zh. Éksp. Teor. Fiz. 7, 469 1958) [Sov. Phys. JETP 34, 322 (1958)] is not active for the lowest-energy modes in the case of the trapping potential because of the discretization of levels.
27. L.D. Landau and E.M. Lifshitz, Statistical Physics, Course of Theoretical Physics (Pergamon Press, Oxford, 1970), Vol. 5.
28. L.P. Pitaevskii, Phys. Lett. A 229, 406 (1997).
29. F. Dalfovo, C. Minniti. and L.P. Pitaevskii, Phys. Rev. A 56, 4855 (1997).
30. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
31. A.A. Abrikosov, L.P. Gorkov, and I. Ye. Dzyaloshinskii, Quantum Field Theoretical Methods in Statistical Physics (Pergamon Press, Oxford, 1965).
32. S. Giorgini, L.P. Pitaevskii, and S. Stringari, J. Low Temp. Phys. 109, 309 (1997).
33. In this paper we do not include the so-called Popov's self-consistent correction in Eq. (1). See, for example, Ref. [27].
34. We have neglected all the transitions that involve the lowest dipole mode (l=1,n=0) because in an external harmonic potential this mode, corresponding to the oscillation of the center of mass, is unaffected by the interatomic forces and then the transition probability due to interaction effects (11) must be zero [19,30]. However, the perturbation formalism we have presented in Sec. III does not take into account this physical consideration automatically and, therefore, we have omitted by hand all transitions with the dipole mode.
35. H. Stoof, J. Low Temp. Phys. 114, 11 (1999).