The European Physical Journal D

, Volume 53, Issue 1, pp 21–26 | Cite as

Exact crossover function for the Casimir force in a non-interacting Bose gas

  • N. BeraEmail author
  • J. K. Bhattacharjee
Molecular Physics and Chemical Physics


An exact calculation of the Casimir force for a non-interacting Bose gas confined between two parallel plates is presented. The gas can be free or trapped, parallel to the plates. Depending on the finite size parameter λ/L (λ is the de Bröglie wavelength and L is the separation of the plates) and the density parameter nλ3 (n, the number density), the Casimir force crosses over from a power law to an exponential fall off is clearly seen. Since the Casimir force measurement requires very small values of L, one needs to take into account of the condensation in a finite system.


05.30.-d Quantum statistical mechanics 05.30.Jp Boson systems 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)Google Scholar
  2. K.A. Milton, J. Phys. A: Math. Gen. 37, R 209 (2004)Google Scholar
  3. K.A. Milton, The Casimir Effect (World Scientific, Singapore, 2001)Google Scholar
  4. V.M. Mostepanen, M.N. Trunov, The Casimir Effect and its Applications (Oxford University Press, New York, 1997)Google Scholar
  5. F.S. Levine, D.A. Micha, Long Range Casimir Forces (Plenum Press, 1993)Google Scholar
  6. G. Plunien, B. Miller, W. Greiner, Phys. Rep. 134, 87 (1986)Google Scholar
  7. M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1994)Google Scholar
  8. M.J. Sparnaay, Physica 24, 751 (1958)Google Scholar
  9. S.K. Lamoreaux, Phys. Rev. Lett. 78, 5 (1997)Google Scholar
  10. U. Mohideen, A. Roy, Phys. Rev. Lett. 81, 4549 (1998)Google Scholar
  11. G. Bressi, G. Carugno, R. Onofrio, G. Ruso, Phys. Rev. Lett. 88, 041804 (2002)Google Scholar
  12. M. Kardar, R. Golestanian, Rev. Mod. Phys. 71, 1233 (1999)Google Scholar
  13. C. Hertlein, A. Gambassi, S. Dietrich, C. Bechinger, Nature Lett. 451, 172 (2008)Google Scholar
  14. A. Ganshin, S. Scheidemantel, R. Garcia, M.H.W. Chan, Phys. Rev. Lett. 97, 075301 (2006)Google Scholar
  15. R. Garcia, M.H.W. Chan, Phys. Rev. Lett. 88, 086101 (2002)Google Scholar
  16. M. Krech, S. Dietrich, Phys. Rev. A 46, 1886 (1992)Google Scholar
  17. R. Zandi, A. Shackell, J. Rudnick, M. Kardar, L.P. Chayes, Phys. Rev. E 76, 030601(R) (2007)Google Scholar
  18. A. Hucht, Phys. Rev. Lett. 99, 185301 (2007)Google Scholar
  19. E.M. Lifshitz, Sov. Phys. JETP 2, 73 (1956)Google Scholar
  20. J. Haro, E. Elizalde, Phys. Rev. Lett. 97, 130401 (2006)Google Scholar
  21. M. Fukoto, Y.F. Yano, P.S. Pershan, Phys. Rev. Lett. 94, 135702 (2005)Google Scholar
  22. D. Dantchev, M. Krech, S. Dietrich, Phys. Rev. E 67, 066120 (2003)Google Scholar
  23. P.A. Martin, V.A. Zagrebnov, Europhys. Lett. 73, 15 (2006)Google Scholar
  24. A. Gambassi, S. Dietrich, Europhys. Lett. 74, 754 (2006)Google Scholar
  25. S. Biswas, Eur. Phys. J. D 42, 109 (2007)Google Scholar
  26. S. Biswas, J. Phys. A: Math. Theor. 40, 9969 (2007)Google Scholar
  27. A. Edery, J. Stat. Mech. P06007 (2002)Google Scholar
  28. R.K. Pathria, Am. J. Phys. 66, 1080 (1998)Google Scholar
  29. W. Ketterle, N.J. van Druten, Phys. Rev. A 54, 656 (1996)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsIndian Association for the Cultivation of Science JadavpurKolkataIndia
  2. 2.Department of Theoretical SciencesS N Bose National Centre for Basic SciencesSalt Lake, KolkataIndia

Personalised recommendations