Abstract
The Casimir effect in a dilute Bose gas confined between two parallel plates is investigated at zero temperature by means of Cornwall–Jackiw–Tomboulis effective action approach within the improved Hartree–Fock approximation in the canonical ensemble, in which the particle number is fixed. In comparison with those in the grand canonical ensemble, where the particle number can be changed, the fixation of the particle number leads to the significant changes in the Casimir energy and the resulting Casimir force. The most interesting result is that the Casimir energy and Casimir force decay in accordance with a half-integer power law instead of an integer power law in the grand canonical ensemble. Moreover, the scattering length dependence of the Casimir force is also considered.
Similar content being viewed by others
References
H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)
T.H. Phat, N.V. Thu, Int. J. Mod. Phys. A 29, 1450078 (2014)
J.F. Babb, Adv. At. Mol. Opt. Phys. 59, 1 (2010)
G. Bimonte, Phys. Rev. A 78, 062101 (2008)
F. Chen, G.L. Klimchitskaya, V.M. Mostepanenko, U. Mohideen, Phys. Rev. B 76, 035338 (2007)
M. Fukuto, Y.F. Yano, P.S. Pershan, Phys. Rev. Lett. 94, 135702 (2005)
A. Ganshin, S. Scheidemantel, R. Garcia, M.H.W. Chan, Phys. Rev. Lett. 97, 075301 (2006)
D.M. Harber, J.M. Obrecht, J.M. McGuirk, E.A. Cornell, Phys. Rev. A 72, 033610 (2005)
J.M. Obrecht, R.J. Wild, M. Antezza, L.P. Pitaevskii, S. Stringari, E.A. Cornell, Phys. Rev. Lett. 98, 063201 (2007)
G.L. Klimchitskaya, V.M. Mostepanenko, J. Phys. A 41, 312002 (2008)
S. Biswas, Eur. Phys. J. D 42, 109 (2007)
S. Biswas, J.K. Bhattacharjee, D. Majumder, K. Saha, N. Chakravarty, J. Phys. B 43, 085305 (2010)
J. Schiefele, C. Henkel, J. Phys. A 42, 045401 (2009)
N. Van Thu, P.T. Song, Physica A 540, 123018 (2020)
N. Van Thu, Phys. Lett. A 382, 1078 (2018)
P.A. Martin, V.A. Zagrebnov, Europhys. Lett. 73, 15 (2006)
M.M. Faruk, S. Biswas, J. Stat. Mech. 043401 (2018)
E. Aydiner, Annalen der Physik 2000178 (2020)
N. Van Thu, L.T. Theu, J. Stat. Phys 168, 1 (2017)
D.C. Roberts, Y. Pomeau, Phys. Rev. Lett. 95, 145303 (2005)
Nguyen Van Thu and Luong Thi Theu, Int. J. Mod. Phys. B 33, 1950114 (2019)
J.M. Cornwall, R. Jackiw, E. Tomboulis, Phys. Rev. D 10, 2428 (1974)
M.E. Fisher, P.G. de Gennes, C.R. Acad, Sci. Paris B 287, 207 (1978)
M. Gross, O. Vasilyev, A. Gambassi, S. Dietrich, Phys. Rev. E 94, 022103 (2016)
C.M. Rohwer, A. Squarcini, O. Vasilyev, S. Dietrich, M. Gross, Phys. Rev. E 99, 062103 (2019)
C.J. Pethick, H. Smith, Bose–Einstein condensation in dilute gases (Cambridge University Press, Cambridge, 2008)
L. Pitaevskii, S. Stringari, Bose–Einstein condensation (Oxford University Press, Oxford, 2003)
J.O. Andersen, Rev. Mod. Phys. 76, 599 (2004)
T.H. Phat, L.V. Hoa, N.T. Anh, N.V. Long, Ann. Phys. 324, 2074 (2009)
Y.B. Ivanov, F. Riek, J. Knoll, Phys. Rev. D 71, 105016 (2005)
S. Floerchinger, C. Wetterich, Phys. Rev. A 79, 013601 (2009)
A. Schmitt, Dense matter in compact stars (Springer, Berlin, 2010)
P.D. Drummond, A. Eleftheriou, K. Huang, K.V. Kheruntsyan, Phys. Rev. A 63, 053602 (2001)
J. Brand, W.P. Reinhardt, J. Phys. B 34, L113 (2001)
A.A. Shams, H.R. Glyde, Phys. Rev. B 79, 214508 (2009)
G.B. Arfken, H.J. Weber, Mathematical methods for physicists, 6th edn. (Academic, San Diego, 2005)
M. Egorov, B. Opanchuk, P. Drummond, B.V. Hall, P. Hannaford, A.I. Sidorov, Phys. Rev. A 87, 053614 (2013)
S. Inouye, M.R. Andrews, J. Stenger, H.-J. Miesner, D.M. Stamper-Kurn, W. Ketterle, Nature (London) 392, 151 (1998)
Acknowledgements
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.01-2018.02.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Van Thu, N. The Casimir Effect in a Dilute Bose Gas in Canonical Ensemble within Improved Hartree–Fock Approximation. J Low Temp Phys 204, 12–23 (2021). https://doi.org/10.1007/s10909-021-02597-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10909-021-02597-5