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Volumn 62, Issue 2, 2000, Pages 1646-1659

Short-range particle correlations in a dilute Bose gas

Author keywords

[No Author keywords available]

Indexed keywords

CHARGED PARTICLES; ELECTRONIC DENSITY OF STATES; KINETIC THEORY OF GASES; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; SPECTRUM ANALYSIS; THERMODYNAMIC PROPERTIES; VARIATIONAL TECHNIQUES;

EID: 0034239251     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.1646     Document Type: Article
Times cited : (30)

References (38)
  • 9
    • 0000724476 scopus 로고
    • S. T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 433 (1958) [Sov. Phys. JETP 7, 299 (1958)]
    • (1958) Sov. Phys. JETP , vol.7 , pp. 299
    • Beliaev, S.T.1
  • 12
    • 0002428394 scopus 로고
    • reprinted in The Many-Body Problem, edited by D. Pines (W. A. Benjamin, New York, 1961)
    • N. N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947),reprinted in The Many-Body Problem, edited by D. Pines (W. A. Benjamin, New York, 1961).
    • (1947) J. Phys. (Moscow) , vol.11 , pp. 23
    • Bogoliubov, N.N.1
  • 16
    • 85036361238 scopus 로고    scopus 로고
    • e-print cond-mat/9807120
    • A. Yu. Cherny, e-print cond-mat/9807120.
    • Yu. Cherny, A.1
  • 18
    • 85036370288 scopus 로고    scopus 로고
    • It is not, of course, the case at nonzero temperatures when spatial boson correlations occur even in the absence of any interaction. Nevertheless, this difference between the zero- and nonzero-temperature situations does not influence the fact that (Formula presented) is connected with the scattering parts of the pair wave functions (3)
    • It is not, of course, the case at nonzero temperatures when spatial boson correlations occur even in the absence of any interaction. Nevertheless, this difference between the zero- and nonzero-temperature situations does not influence the fact that (Formula presented) is connected with the scattering parts of the pair wave functions (3).
  • 19
    • 85036397050 scopus 로고    scopus 로고
    • By the leading order in (Formula presented) we mean zero depletion of the condensate: (Formula presented)
    • By the leading order in (Formula presented) we mean zero depletion of the condensate: (Formula presented).
  • 25
    • 85036331480 scopus 로고    scopus 로고
    • This can always be achieved with a global gauge transformation of the Bose operators (Formula presented) and (Formula presented) provided there are no magnetic fields (see, e.g., Ref. 8
    • This can always be achieved with a global gauge transformation of the Bose operators (Formula presented) and (Formula presented) provided there are no magnetic fields (see, e.g., Ref. 8).
  • 26
    • 85036341239 scopus 로고    scopus 로고
    • Using formula (5.12) of the paper of Hugenholtz and Pines 4 together with the relations (4.4) of the paper of Beliaev 4, for (Formula presented) one can derive (Formula presented) where (Formula presented) is the Fourier transform of (Formula presented) and (Formula presented). So, using the definition of the structure factor, one can arrive at (Formula presented) for (Formula presented). Here for (Formula presented) we have (Formula presented), which can be rewritten in the form of Eq. (9)
    • Using formula (5.12) of the paper of Hugenholtz and Pines 4 together with the relations (4.4) of the paper of Beliaev 4, for (Formula presented) one can derive (Formula presented) where (Formula presented) is the Fourier transform of (Formula presented) and (Formula presented). So, using the definition of the structure factor, one can arrive at (Formula presented) for (Formula presented). Here for (Formula presented) we have (Formula presented), which can be rewritten in the form of Eq. (9).
  • 28
    • 85036421894 scopus 로고    scopus 로고
    • We stress that the potential is involved through the mediation of the scattering length (11) only in the first few terms in the low-density expansions. For the high-order terms the dependence on a specific shape of the potential should appear
    • We stress that the potential is involved through the mediation of the scattering length (11) only in the first few terms in the low-density expansions. For the high-order terms the dependence on a specific shape of the potential should appear.
  • 29
    • 85036228805 scopus 로고    scopus 로고
    • The Bogoliubov model, which is in fact perturbation theory with respect to the coupling constant (Formula presented), provides accuracy up to the last term in Eq. (42) proportional to (Formula presented) 22. For this reason, in the expansion (42) there is no (Formula presented) term proportional to (Formula presented)
    • The Bogoliubov model, which is in fact perturbation theory with respect to the coupling constant (Formula presented), provides accuracy up to the last term in Eq. (42) proportional to (Formula presented) 22. For this reason, in the expansion (42) there is no (Formula presented) term proportional to (Formula presented).
  • 30
    • 36149018678 scopus 로고
    • T. T. Wu, Phys. Rev. 115, 1390 (1959).
    • (1959) Phys. Rev. , vol.115 , pp. 1390
    • Wu, T.T.1
  • 31
    • 85036166846 scopus 로고
    • V. V. Tolmachev, Dokl. Akad. Nauk. (SSSR) 135, 41 (1960) [ Sov. Phys. Dokl. 5, 1190 (1960)].
    • (1960) Sov. Phys. Dokl. , vol.5 , pp. 1190
    • Tolmachev, V.V.1
  • 32
    • 85036149224 scopus 로고    scopus 로고
    • For example, this can be shown as follows. For a strongly singular potential (Formula presented) for (Formula presented) we have (Formula presented) and (Formula presented), which in conjunction with Eqs. (3) and (4) leads to (Formula presented) and (Formula presented). So (Formula presented)
    • For example, this can be shown as follows. For a strongly singular potential (Formula presented) for (Formula presented) we have (Formula presented) and (Formula presented), which in conjunction with Eqs. (3) and (4) leads to (Formula presented) and (Formula presented). So (Formula presented).
  • 33
    • 85036141414 scopus 로고    scopus 로고
    • Note that Eq. (67) can help to derive the strong-coupling generalization of the Gross-Pitaevskii equation on a solid theoretical basis beyond any effective-interaction picture
    • Note that Eq. (67) can help to derive the strong-coupling generalization of the Gross-Pitaevskii equation on a solid theoretical basis beyond any effective-interaction picture.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.