Abstract
By means of the quantum field theory, the Casimir effect in an interacting Bose gas confined between two parallel plates is considered in the one-loop approximation. The Casimir effect due to the quantum fluctuations and thermal fluctuations is calculated associated with the periodic boundary condition applied at the plates. Our results show that the Casimir force is short-ranged in every ranges of the temperature.
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References
H.B.G. Casimir, D. Polder, Phys. Rev. 73, 360 (1948)
H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)
M.J. Sparnaay, Measurements of attractive forces between flat plates. Physica 24, 751 (1958)
M. Bordag, U. Mohideen, V.M. Mostepanenko, Phys. Rep. 353, 1 (2001)
J.F. Babb, Adva. Atom. Mol. Opt. Phys. 59, 1 (2010)
B.S. Kay, Phys. Rev. D 20, 3052 (1979)
V.M. Mostepanenko, N.N. Trunov, Usp. Fiz. Nauk 156, 385–426 (1988)
T.H. Phat, N. Van Thu, Int. J. Mod. Phys. A 29, 1450078 (2014)
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)
N.V. Thu, Phys. Lett. A 382, 1078–1084 (2018)
N. Van Thu, P.T. Song, Physica A 540, 123018 (2020)
P.A. Martin, V.A. Zagrebnov, Europhys. Lett. 73, 15 (2006)
M.M. Faruk, S. Biswas, J. Stat. Mech. 2018, 043401 (2018)
E. Aydiner, Annalen der Physik 532, 2000178 (2020)
J. Schiefele, C. Henkel, J. Phys. A 42, 045401 (2009)
S. Biswas, J.K. Bhattacharjee, D. Majumder, K. Saha, N. Chakravarty, J. Phys. B 43, 085305 (2010)
S. Biswas, J. Phys. A 40, 9969 (2007)
D.C. Roberts, Y. Pomeau, Phys. Rev. Lett. 95, 145303 (2005)
N. Van Thu, L.T. Theu, D.T. Hai, J. Exp. Theor. Phys. 130, 321 (2020)
N.V. Thu, L.T. Theu, J. Stat. Phys. 168, 1–10 (2017)
N.V. Thu, L.T. Theu, Int. J. Mod. Phys. B 33, 1950114 (2019)
S. Sachdev, Quantum Phase Transition (Cambridge University Press, Cambridge, 2012)
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)
S. Floerchinger, C. Wetterich, Phys. Rev. A 79, 013601 (2009)
A. Schmitt, Dense Matter in Compact Stars (Springer, Berlin, 2010)
N.V. Thu, T.H. Phat, P.T. Song, J. Low Temp. Phys. 186, 127 (2017)
A. A. Saharian, arXiv:0708.1187
A. Edery, J. Stat. Mech. 2006, P06007 (2006)
Bert Van Schaeybroeck, Physica A 392, 3806 (2013)
G. Baym, J.-P. Blaizot, M. Holzmann, F. Lalu, D. Vautherin, Phys. Rev. Lett. 83, 1703 (1999)
N. Van Thu, P.T. Song, in preparation
M. Napiorkowski, J. Piasecki, Phys. Rev. E 84, 061105 (2011)
Acknowledgements
This research is funded by Ministry of Education and Training of Vietnam under Grant No. B2018-TTB-12 - CTrVL.
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Song, P.T., Van Thu, N. The Casimir Effect in a Weakly Interacting Bose Gas. J Low Temp Phys 202, 160–174 (2021). https://doi.org/10.1007/s10909-020-02535-x
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DOI: https://doi.org/10.1007/s10909-020-02535-x