Skip to main content
SpringerLink
Log in

On the Ground-State Energy and Local Pressure of an Inhomogeneous Bose Gas

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

The exact expression for the average kinetic energy of an inhomogeneous Bose gas in the ground state is obtained as a functional of the inhomogeneous density of the Bose–Einstein condensate. The result is based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose–Einstein condensate. This makes it possible to avoid the use of anomalous averages. On this basis, the explicit expressions for the ground-state energy and the local pressure of an inhomogeneous Bose gas are derived within the self-consistent Hartree–Fock approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)

    Article  ADS  Google Scholar 

  2. E.A. Cornell, C.E. Wieman, Rev. Mod. Phys. 74, 875 (2002)

    Article  ADS  Google Scholar 

  3. N. Navon, S. Piatecki, K. Günter, B. Rem, T.C. Nguyen, F. Chevy, W. Krauth, C. Salomon, Phys. Rev. Lett. 107, 135301 (2011)

    Article  ADS  Google Scholar 

  4. T.-L. Ho, Q. Zhou, Nature 463, 1057 (2010)

    Article  Google Scholar 

  5. L.D. Landau, E.M. Lifshitz, Statistical Physics, Part 1 (Butterworth-Heinemann, Oxford, 1980)

    Google Scholar 

  6. N.N. Bogoliubov, J. Phys. USSR 11, 23 (1947)

    Google Scholar 

  7. E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, Part 2: Theory of the Condensed State (Butterworth-Heinemann, Oxford, 1980)

    Google Scholar 

  8. N.N. Bogolubov, N.N. Bogolubov Jr., Introduction to Quantum Statistical Mechanics (Gordon and Breach, New York, 1992)

    MATH  Google Scholar 

  9. L.P. Pitaevskii, Phys. Usp. 41, 569 (1998)

    Article  Google Scholar 

  10. E.P. Gross, Nuovo Cimento 20, 454 (1961)

    Article  Google Scholar 

  11. L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961)

    MathSciNet  Google Scholar 

  12. L.P. Pitaevskii, Phys. Usp. 49, 333 (2006)

    Article  ADS  Google Scholar 

  13. E.H. Lieb, R. Seiringer, J. Yngvason, Phys. Rev. A 61, 043602 (2000)

    Article  ADS  Google Scholar 

  14. W.H. Bassichis, L.L. Foldy, Phys. Rev. A 133, 435 (1964)

    Article  Google Scholar 

  15. H. Stolz, Phys. A 86, 11 (1977)

    Article  Google Scholar 

  16. C.-H. Zhang, H.A. Fertig, Phys. Rev. A 74, 023613 (2006)

    Article  ADS  Google Scholar 

  17. P. Navez, K. Bongs, Europhys. Lett. 88, 60008 (2009)

    Article  ADS  Google Scholar 

  18. V.B. Bobrov, S.A. Trigger, I.M. Yurin, Phys. Lett. A 374, 1938 (2010)

    Article  ADS  Google Scholar 

  19. A.M. Ettouhami, Prog. Theor. Phys. 127, 453 (2012)

    Article  ADS  Google Scholar 

  20. V.B. Bobrov, S.A. Trigger, J. Low Temp. Phys. 170, 31 (2013)

    Article  ADS  Google Scholar 

  21. V.B. Bobrov, S.A. Triger, P. Schram, JETP 80, 853 (1995)

    ADS  Google Scholar 

  22. V.B. Bobrov, S.A. Trigger, Bull. Lebedev Phys. Inst. 42, 13 (2015)

    Article  ADS  Google Scholar 

  23. V.B. Bobrov, S.A. Trigger, A.G. Zagorodny, Low Temp. Phys. 41, 902 (2015)

    ADS  Google Scholar 

  24. L.P. Kadanoff, G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962)

    MATH  Google Scholar 

  25. V.B. Bobrov, S.A. Trigger, A. Zagorodny, Phys. Rev. A 82, 044105 (2010)

    Article  ADS  Google Scholar 

  26. V.L. Ginzburg, L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950) (English transl.: L. D. Landau, Collected papers. Pergamon, Oxford (1965), p. 546)

  27. O. Penrose, L. Onsager, Phys. Rev. 104, 576 (1956)

    Article  ADS  Google Scholar 

  28. C.N. Yang, Rev. Mod. Phys. 34, 694 (1962)

    Article  ADS  Google Scholar 

  29. V.B. Bobrov, S.A. Trigger, A.G. Zagorodny, Dokl. Phys. 60, 147 (2015)

    Article  ADS  Google Scholar 

  30. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)

    Article  ADS  Google Scholar 

  31. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  32. R.O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989)

    Article  ADS  Google Scholar 

  33. D.N. Zubarev, Nonequilibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974)

    Google Scholar 

  34. B.V. Vasil’ev, V.L. Lyuboshits, Phys. Usp. 37, 345 (1994)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The authors are grateful to A.G. Khrapak, A.A. Rukhadze, P.P.J.M. Schram, and A.G. Zagorodny for helpful discussions. This study was supported by the Russian Science Foundation, Project No. 14-19-01492.

Author information

Authors and Affiliations

  1. Joint Institute for High Temperatures, Russian Academy of Sciences, 13/19, Izhorskaia Str., Moscow, Russia, 125412

    V. B. Bobrov & S. A. Trigger

Authors
  1. V. B. Bobrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Trigger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Trigger.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bobrov, V.B., Trigger, S.A. On the Ground-State Energy and Local Pressure of an Inhomogeneous Bose Gas. J Low Temp Phys 186, 1–9 (2017). https://doi.org/10.1007/s10909-016-1671-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-016-1671-0

Keywords

Search

Navigation