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The Landau damping and frequency-shift of monopole mode in an elongated-rubidium Bose-Einstein condensate are investigated by using the time-dependent Hartree-Fock-Bogoliubov approximation. Improving the previous approach, We have taken into account the practical relaxations of elementary excitations and the orthogonal relation among them. With such an approach, we provide a new calculation formula for Landau damping rate and frequency-shift. In addition, our previous method of eliminating the divergence in three-mode coupling matrix elements is also improved by zeroing the kinetic energy at the condensate boundary instead of minimizing the ground-state energy. Based on these improvements, both the Landau damping rate and the frequency-shift of the monopole mode are analytically calculated and their temperature dependences are also discussed. And all the theoretical results are in agree meat with experimental data.
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Keywords:
- Bose-Einstein condensate /
- Landau damping and frequency-shift /
- Hartree-Fock-Bogoliubov approximation /
- Thomas-Fermi approximation
[1] Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (2nd Edn.) (Cambridge University Press)
[2] Stringari S 1996 Phys. Rev. Lett. 77 2360
[3] Fetter A L 1996 Phys. Rev. A 53 4245
[4] Ruprecht P A, Edwards M, Burnett K, Clark C W 1996 Phys. Rev. A 54 4178
[5] Dalfovo F, Minniti C, Pitaevskii L P 1997 Phys. Rev. A 56 4855
[6] Morgan S A, Choi S, Burnett K, Edwards M 1998 Phys. Rev. A 57 3818
[7] Hechenblaikner G, Maragó O M, Hodby E, Arlt J, Hopkins S, Foot C J 2000 Phys. Rev. Lett. 85 692
[8] Hodby E, Maragó O M, Hechenblaikner G, Foot C J 2001 Phys. Rev. Lett. 86 2196
[9] Maragó O M, Hopkins S A, Arlt J, Hodby E, Hechenblaikner G, Foot C J 2000 Phys. Rev. Lett. 84 2056
[10] Khawaja U Al, Stoof H T C 2001 Phys. Rev. A 65 013605
[11] Hechenblaikner G, Morgan S A, Hodby E, Maragó O M, Foot C J 2002 Phys. Rev. A 65 033612
[12] Liu W M, Fan W B, Zheng W M, Liang J Q, Chui S T 2002 Phys. Rev. Lett. 88 170408
[13] Ma Y L, Chui S T 2002 Phys. Rev. A 65 053610
[14] Hu B, Huang G, Ma Y L 2004 Phys. Rev. A 69 063608
[15] Huang G, Szeftel J, Zhu S 2002 Phys. Rev. A 65 053605
[16] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[17] Jin D S, Matthews M R, Ensher J R, Wieman C E, Cornell E A 1997 Phys. Rev. Lett. 78 764
[18] Jin D S, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1996 Phys. Rev. Lett. 77 420
[19] Chevy F, Bretin V, Rosenbusch P, Madison K W, Dalibard J 2002 Phys. Rev. Lett. 88 250402
[20] Stamper-Kurn D M, Miesner H J, Inouye S, Andrews M R, Ketterle W 1998 Phys.Rev. Lett. 81 500
[21] Onofrio R, Durfee D S, Raman C, Köhl M, Kuklewicz C E, Ketterle W 2000 Phys. Rev. Lett. 84 810
[22] Maragó O, Hechenblaikner J, Hodby E, Foot C 2001 Phys. Rev. Lett. 86 3938
[23] Mewes M O, Andrews M R, Druten N J V, Kurn D M, Durfee D S, Townsend C G, Ketterle W 1996 Phys. Rev. Lett. 77 988
[24] Zaremba E, Griffin A, Nikuni T 1998 Phys. Rev. A 57 4695
[25] Zaremba E, Nikuni T, Griffin A 1999 J. Low Temp. Phys. 116 277
[26] Jackson B, Zaremba E 2002 Phys. Rev. Lett. 88 180402
[27] Jackson B, Zaremba E 2002 Phys. Rev. Lett. 89 150402
[28] Morgan S A, Rusch M, Hutchinson D A W, Burnett K 2003 Phys. Rev. Lett. 91 250403
[29] Morgan S A 2004 Phys. Rev. A 69 023609
[30] Giorgini S 1998 Phys. Rev. A 57 2949
[31] Giorgini S 2000 Phys. Rev. A 61 063615
[32] Pitaevskii L P, Stringari S 1997 Phys. Lett. A 235 398
[33] Fedichev P O, Shlyapnikov G V, Walraven J T M 1998 Phys. Rev. Lett. 80 2269
[34] Reidl J, Csordás A, Graham R, Szépfalusy P 2000 Phys. Rev. A 61 043606
[35] Tsuchiya S, Griffin A 2005 Phys. Rev. A 72 053621
[36] Guilleumas M, Pitaevskii L P 2003 Phys. Rev. A 67 053607
[37] Guilleumas M, Pitaevskii L P 1999 Phys. Rev. A 61 013602
[38] Ma X, Ma Y L, Huang G 2007 Phys. Rev. A 75 013628
[39] Ma X, Zhou Y, Ma Y L, Huang G 2006 Chin. Phys. 15 1871
[40] Ma X, Ma Y L, Huang G 2007 Chin. Phys. Lett. 24 616
[41] Ma X, Yang Z, Lu J, Wei W 2011 Chin. Phys. B 20 070307
[42] Yang Z, Chai Z, Li C, Ma X 2012 Commun. Theor. Phys. 57 789
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[1] Pethick C J, Smith H 2008 Bose-Einstein Condensation in Dilute Gases (2nd Edn.) (Cambridge University Press)
[2] Stringari S 1996 Phys. Rev. Lett. 77 2360
[3] Fetter A L 1996 Phys. Rev. A 53 4245
[4] Ruprecht P A, Edwards M, Burnett K, Clark C W 1996 Phys. Rev. A 54 4178
[5] Dalfovo F, Minniti C, Pitaevskii L P 1997 Phys. Rev. A 56 4855
[6] Morgan S A, Choi S, Burnett K, Edwards M 1998 Phys. Rev. A 57 3818
[7] Hechenblaikner G, Maragó O M, Hodby E, Arlt J, Hopkins S, Foot C J 2000 Phys. Rev. Lett. 85 692
[8] Hodby E, Maragó O M, Hechenblaikner G, Foot C J 2001 Phys. Rev. Lett. 86 2196
[9] Maragó O M, Hopkins S A, Arlt J, Hodby E, Hechenblaikner G, Foot C J 2000 Phys. Rev. Lett. 84 2056
[10] Khawaja U Al, Stoof H T C 2001 Phys. Rev. A 65 013605
[11] Hechenblaikner G, Morgan S A, Hodby E, Maragó O M, Foot C J 2002 Phys. Rev. A 65 033612
[12] Liu W M, Fan W B, Zheng W M, Liang J Q, Chui S T 2002 Phys. Rev. Lett. 88 170408
[13] Ma Y L, Chui S T 2002 Phys. Rev. A 65 053610
[14] Hu B, Huang G, Ma Y L 2004 Phys. Rev. A 69 063608
[15] Huang G, Szeftel J, Zhu S 2002 Phys. Rev. A 65 053605
[16] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[17] Jin D S, Matthews M R, Ensher J R, Wieman C E, Cornell E A 1997 Phys. Rev. Lett. 78 764
[18] Jin D S, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1996 Phys. Rev. Lett. 77 420
[19] Chevy F, Bretin V, Rosenbusch P, Madison K W, Dalibard J 2002 Phys. Rev. Lett. 88 250402
[20] Stamper-Kurn D M, Miesner H J, Inouye S, Andrews M R, Ketterle W 1998 Phys.Rev. Lett. 81 500
[21] Onofrio R, Durfee D S, Raman C, Köhl M, Kuklewicz C E, Ketterle W 2000 Phys. Rev. Lett. 84 810
[22] Maragó O, Hechenblaikner J, Hodby E, Foot C 2001 Phys. Rev. Lett. 86 3938
[23] Mewes M O, Andrews M R, Druten N J V, Kurn D M, Durfee D S, Townsend C G, Ketterle W 1996 Phys. Rev. Lett. 77 988
[24] Zaremba E, Griffin A, Nikuni T 1998 Phys. Rev. A 57 4695
[25] Zaremba E, Nikuni T, Griffin A 1999 J. Low Temp. Phys. 116 277
[26] Jackson B, Zaremba E 2002 Phys. Rev. Lett. 88 180402
[27] Jackson B, Zaremba E 2002 Phys. Rev. Lett. 89 150402
[28] Morgan S A, Rusch M, Hutchinson D A W, Burnett K 2003 Phys. Rev. Lett. 91 250403
[29] Morgan S A 2004 Phys. Rev. A 69 023609
[30] Giorgini S 1998 Phys. Rev. A 57 2949
[31] Giorgini S 2000 Phys. Rev. A 61 063615
[32] Pitaevskii L P, Stringari S 1997 Phys. Lett. A 235 398
[33] Fedichev P O, Shlyapnikov G V, Walraven J T M 1998 Phys. Rev. Lett. 80 2269
[34] Reidl J, Csordás A, Graham R, Szépfalusy P 2000 Phys. Rev. A 61 043606
[35] Tsuchiya S, Griffin A 2005 Phys. Rev. A 72 053621
[36] Guilleumas M, Pitaevskii L P 2003 Phys. Rev. A 67 053607
[37] Guilleumas M, Pitaevskii L P 1999 Phys. Rev. A 61 013602
[38] Ma X, Ma Y L, Huang G 2007 Phys. Rev. A 75 013628
[39] Ma X, Zhou Y, Ma Y L, Huang G 2006 Chin. Phys. 15 1871
[40] Ma X, Ma Y L, Huang G 2007 Chin. Phys. Lett. 24 616
[41] Ma X, Yang Z, Lu J, Wei W 2011 Chin. Phys. B 20 070307
[42] Yang Z, Chai Z, Li C, Ma X 2012 Commun. Theor. Phys. 57 789
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