메뉴 건너뛰기




Volumn 70, Issue 4, 2004, Pages

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; DENSITY OF GASES; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON TRAPS; FUNCTIONS; GROUND STATE; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBLEM SOLVING; STATISTICAL METHODS; THEOREM PROVING; VARIATIONAL TECHNIQUES; WAVE EQUATIONS;

EID: 19744382534     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.043622     Document Type: Article
Times cited : (19)

References (88)
  • 1
    • 51249193203 scopus 로고
    • E.P. Gross, Nuovo Cimento 20, 454 (1961); J. Math. Phys. 4, 195 (1963); L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
    • (1961) Nuovo Cimento , vol.20 , pp. 454
    • Gross, E.P.1
  • 2
    • 0000394530 scopus 로고
    • E.P. Gross, Nuovo Cimento 20, 454 (1961); J. Math. Phys. 4, 195 (1963); L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
    • (1963) J. Math. Phys. , vol.4 , pp. 195
  • 3
    • 51249193203 scopus 로고
    • E.P. Gross, Nuovo Cimento 20, 454 (1961); J. Math. Phys. 4, 195 (1963); L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
    • (1961) Zh. Eksp. Teor. Fiz. , vol.40 , pp. 646
    • Pitaevskii, L.P.1
  • 4
    • 51249193203 scopus 로고
    • E.P. Gross, Nuovo Cimento 20, 454 (1961); J. Math. Phys. 4, 195 (1963); L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
    • (1961) Sov. Phys. JETP , vol.13 , pp. 451
  • 7
  • 10
    • 0002428394 scopus 로고
    • N.N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947); reprinted in The Many-Body Problem, edited by D. Pines (Benjamin, New York, 1961)
    • (1947) J. Phys. (Moscow) , vol.11 , pp. 23
    • Bogoliubov, N.N.1
  • 11
    • 0003585224 scopus 로고
    • reprinted in Benjamin, New York
    • N.N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947); reprinted in The Many-Body Problem, edited by D. Pines (Benjamin, New York, 1961)
    • (1961) The Many-body Problem
    • Pines, D.1
  • 12
    • 36149004969 scopus 로고
    • T.D. Lee, K. Huang, and C.N. Yang, Phys. Rev. 106, 1135 (1957); K.A. Brueckner and K. Sawada, ibid. 106, 1117 (1957).
    • (1957) Phys. Rev. , vol.106 , pp. 1135
    • Lee, T.D.1    Huang, K.2    Yang, C.N.3
  • 13
    • 0001742041 scopus 로고
    • T.D. Lee, K. Huang, and C.N. Yang, Phys. Rev. 106, 1135 (1957); K.A. Brueckner and K. Sawada, ibid. 106, 1117 (1957).
    • (1957) Phys. Rev. , vol.106 , pp. 1117
    • Brueckner, K.A.1    Sawada, K.2
  • 16
    • 0038429687 scopus 로고
    • V.N. Popov, Theor. Math. Phys. 11, 354 (1971); [Theor. Math. Phys. 11, 565 (1972)]; see Eq. 3.15 at zero temperature. The T-matrix at low energies should be rewritten in terms of the 2D scattering length.
    • (1971) Theor. Math. Phys. , vol.11 , pp. 354
    • Popov, V.N.1
  • 17
    • 6144245310 scopus 로고
    • V.N. Popov, Theor. Math. Phys. 11, 354 (1971); [Theor. Math. Phys. 11, 565 (1972)]; see Eq. 3.15 at zero temperature. The T-matrix at low energies should be rewritten in terms of the 2D scattering length.
    • (1972) Theor. Math. Phys. , vol.11 , pp. 565
  • 21
    • 0347107495 scopus 로고    scopus 로고
    • E.H. Lieb, R. Seiringer, and J. Yngvason, Phys. Rev. A 61, 043602 (2000); Commun. Math. Phys. 224, 17 (2001); Phys. Rev. Lett. 91, 150401 (2003); E.H. Lieb and R. Seiringer, ibid. 88, 170409 (2002).
    • (2000) Phys. Rev. A , vol.61 , pp. 043602
    • Lieb, E.H.1    Seiringer, R.2    Yngvason, J.3
  • 22
    • 84894373577 scopus 로고    scopus 로고
    • E.H. Lieb, R. Seiringer, and J. Yngvason, Phys. Rev. A 61, 043602 (2000); Commun. Math. Phys. 224, 17 (2001); Phys. Rev. Lett. 91, 150401 (2003); E.H. Lieb and R. Seiringer, ibid. 88, 170409 (2002).
    • (2001) Commun. Math. Phys. , vol.224 , pp. 17
  • 23
    • 0942277916 scopus 로고    scopus 로고
    • E.H. Lieb, R. Seiringer, and J. Yngvason, Phys. Rev. A 61, 043602 (2000); Commun. Math. Phys. 224, 17 (2001); Phys. Rev. Lett. 91, 150401 (2003); E.H. Lieb and R. Seiringer, ibid. 88, 170409 (2002).
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 150401
  • 24
    • 0037193018 scopus 로고    scopus 로고
    • E.H. Lieb, R. Seiringer, and J. Yngvason, Phys. Rev. A 61, 043602 (2000); Commun. Math. Phys. 224, 17 (2001); Phys. Rev. Lett. 91, 150401 (2003); E.H. Lieb and R. Seiringer, ibid. 88, 170409 (2002).
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 170409
    • Lieb, E.H.1    Seiringer, R.2
  • 25
    • 85015785209 scopus 로고    scopus 로고
    • A.Yu. Cherny, cond-mat/9807120
    • A.Yu. Cherny, cond-mat/9807120.
  • 27
    • 0034239251 scopus 로고    scopus 로고
    • A.Yu. Cherny and A.A. Shanenko, Phys. Rev. E 62, 1646 (2000); 60, R5 (1999).
    • (1999) Phys. Rev. E , vol.60
  • 29
    • 85015779146 scopus 로고    scopus 로고
    • note
    • We call the potential weak coupling if it is small and integrable; for more discussions, see Ref. [16].
  • 42
    • 0035920760 scopus 로고    scopus 로고
    • A. Görlitz, J.M. Vogels, A.E. Leanhardt, C. Raman, T.L. Gustavson, J.R. Abo-Shaeer, A.P. Chikkatur, S. Gupta, S. Inouye, T.P. Rosenband, and W. Ketterle, Phys. Rev. Lett. 87, 130402 (2001); F. Schreck et al., ibid. 87, 080403 (2001); M. Greiner et al., ibid. 87, 160405 (2001).
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 080403
    • Schreck, F.1
  • 43
    • 37649033096 scopus 로고    scopus 로고
    • A. Görlitz, J.M. Vogels, A.E. Leanhardt, C. Raman, T.L. Gustavson, J.R. Abo-Shaeer, A.P. Chikkatur, S. Gupta, S. Inouye, T.P. Rosenband, and W. Ketterle, Phys. Rev. Lett. 87, 130402 (2001); F. Schreck et al., ibid. 87, 080403 (2001); M. Greiner et al., ibid. 87, 160405 (2001).
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 160405
    • Greiner, M.1
  • 47
    • 85015716426 scopus 로고    scopus 로고
    • note
    • In this paper we use the definition ζ=Plankv;/√ μm for the coherence or healing length as in Refs. [35,44] whereas [3] uses ζ = ℏ/√2 μm.
  • 49
    • 0035396370 scopus 로고    scopus 로고
    • D.S. Petrov, M. Holzmann, and G.V. Shlyapnikov, Phys. Rev. Lett. 84, 2551 (2000); D.S. Petrov and G.V. Shlyapnikov, Phys. Rev. A 64, 012706 (2001).
    • (2001) Phys. Rev. A , vol.64 , pp. 012706
    • Petrov, D.S.1    Shlyapnikov, G.V.2
  • 55
    • 0346362491 scopus 로고    scopus 로고
    • S. Jochim et al., Science 302, 2101 (2003).
    • (2003) Science , vol.302 , pp. 2101
    • Jochim, S.1
  • 65
    • 0003399309 scopus 로고
    • N.N. Bogoliubov, Phys. Abhandl. SU 6, 1 (1962); 6, 113 (1962); 6, 229 (1962); reprinted in N.N. Bogoliubov, Lectures on Quantum Statistics, (Gordon and Breach, New York, 1970), Vol. 2, p. 1.
    • (1962) Phys. Abhandl. SU , vol.6 , pp. 1
    • Bogoliubov, N.N.1
  • 66
    • 0000653968 scopus 로고
    • N.N. Bogoliubov, Phys. Abhandl. SU 6, 1 (1962); 6, 113 (1962); 6, 229 (1962); reprinted in N.N. Bogoliubov, Lectures on Quantum Statistics, (Gordon and Breach, New York, 1970), Vol. 2, p. 1.
    • (1962) Phys. Abhandl. SU , vol.6 , pp. 113
  • 67
    • 0004593921 scopus 로고
    • N.N. Bogoliubov, Phys. Abhandl. SU 6, 1 (1962); 6, 113 (1962); 6, 229 (1962); reprinted in N.N. Bogoliubov, Lectures on Quantum Statistics, (Gordon and Breach, New York, 1970), Vol. 2, p. 1.
    • (1962) Phys. Abhandl. SU , vol.6 , pp. 229
  • 68
    • 0002709629 scopus 로고
    • reprinted in Gordon and Breach, New York
    • N.N. Bogoliubov, Phys. Abhandl. SU 6, 1 (1962); 6, 113 (1962); 6, 229 (1962); reprinted in N.N. Bogoliubov, Lectures on Quantum Statistics, (Gordon and Breach, New York, 1970), Vol. 2, p. 1.
    • (1970) Lectures on Quantum Statistics , vol.2 , pp. 1
    • Bogoliubov, N.N.1
  • 69
    • 0001053337 scopus 로고    scopus 로고
    • For simplicity we use here the approach of broken global gauge symmetry. Approaches based on number conservation have been shown to be feasible [see, e.g., Y. Castin and R. Dum, Phys. Rev. A 57, 3008 (1998)] and should yield the same results.
    • (1998) Phys. Rev. A , vol.57 , pp. 3008
    • Castin, Y.1    Dum, R.2
  • 70
    • 4243364613 scopus 로고    scopus 로고
    • 2)) describes the bound state of two fermions in a superfluid Fermi system. See Ref. [50] and A.Yu. Cherny and A.A. Shanenko, Phys. Rev. B 60, 1276 (1999).
    • (1999) Phys. Rev. B , vol.60 , pp. 1276
    • Cherny, A.Yu.1    Shanenko, A.A.2
  • 78
    • 85015716599 scopus 로고    scopus 로고
    • note
    • Due to criterion (58) the expression for the chemical potential (57) is not valid formally at very low densities. However, we arrive at the same result if we calculate first the interaction energy directly from Eqs. (11), (54), and (56), and then integrate over λ using the relation (63).
  • 80
    • 1342313863 scopus 로고
    • V.S. Popov, A.E. Kudryavtsev, and V.D. Mur, Zh. Eksp. Teor. Fiz. 77, 1727 (1979) [Sov. Phys. JETP 50, 865 (1979)].
    • (1979) Sov. Phys. JETP , vol.50 , pp. 865
  • 81
    • 85015755918 scopus 로고    scopus 로고
    • S. Sinha and J. Brand (unpublished)
    • S. Sinha and J. Brand (unpublished).
  • 85
    • 10044291281 scopus 로고
    • N.N. Bogoliubov, Usp. Fiz. Nauk 67, 549 (1959) [Sov. Phys. Usp. 2, 2 (1959)].
    • (1959) Sov. Phys. Usp. , vol.2 , pp. 2
  • 86
    • 85015752563 scopus 로고    scopus 로고
    • note
    • The noncondensate fraction was referred to as "supracondensate" in Refs. [15-17].


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.