Condensate Density of a Bose Gas Confined between Two Parallel Plates in Canonical Ensemble within Improved Hartree-Fock Approximation
Main Article Content
Abstract
By means of Cornwall-Jackiw-Tomboulis (CJT) effective action approach, the condensate density of a dilute Bose gas is investigated in the canonical ensemble. Our results show that the condensate density is proportional to a half-integer power law of the s-wave scattering length and distance between two plates. Apart from that, these quantities also depend on the particle number and area of each plate.
Keywords:
Condensate density, dilute Bose gas, improved Hatree-Fock approximation, canonical ensemble
References
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[3] L.P. Pitaevskii, Vortex lines in an imperfect Bose gas, Sov. Phys. JETP. 13 (1961) 451-454.
[4] P. Ao, S.T. Chui, Binary Bose-Einstein condensate mixtures in weakly and strongly segregated phases, Physical Review A. 58 (1998) 4836-4840. https://doi.org/10.1103/PhysRevA.58.4836.
[5] R.A. Barankov, Boundary of two mixed Bose-Einstein condensates, Physical Review A. 66(2002) 013612(1) - 013612(6). https://doi.org/10.1103/PhysRevA.66.013612.
[6] I.E. Mazets, Waves on an interface between two phase-separated Bose-Einstein condensates, Physical Review A. 65 (2002) 033618(1)-033618(5). https://doi.org/10.1103/PhysRevA.65.033618.
[7] J.O. Indekeu, C.J. Lin, N.V. Thu, B.V. Schaeybroeck, T.H. Phat, Static interfacial properties of Bose-Einstein-condensate mixtures, Physical Review A. 91 (2015) 033615(1)-033615(10). https://doi.org/10.1103/PhysRevA.91.033615
[8] L.P. Pitaevskii, S. Stringari, Bose-Einstein Condensation, Oxford: Oxford University Press, 2003.
[9] C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge: Cambridge University Pres, 2008.
[10] N.N. Bogolyubov, On the theory of superfluidity, J. Phys. (USSR). 11 (1947) 23-36.
[11] J.M. Cornwall, R. Jackiw, E. Tomboulis, Effecitve action composite operators, Physical Review D. 10 (1974). 2428-2445. https://doi.org/10.1103/PhysRevD.10.2428.
[12] N.V. Thu, P.T. Song, Casimir effect in a weakly interacting Bose gas confined by a parallel plate geometry in improved Hartree–Fock, Physica A. 540 (2020) 123018(1)-123018(9). https://doi.org/10.1016/j.physa.2019.123018.
[13] N.V. Thu, L.T. Theu, Finite-size effect on Bose Einstein condensate mixtures in improved Hartree Fock approximation, International Journal of Modern Physics B. 33 (2019) 1950114(1)-1950114(10). https://doi.org/10.1142/S0217979219501145.
[14] N.V. Thu, Density of condensate of a weakly interacting Bose gas confined between two hard walls in improved Hartree-Fock approximation, DLU Journal of Science. 10 (2020) 94-104. http://dx.doi.org/10.37569/DalatUniversity.10.2.579(2020).
[15] N.V. Thu, L.T. Theu, D.T. Hai, Casimir and Surface Tension Forces on a Single Interacting Bose–Einstein Condensate in Canonical Ensemble, Journal of Experimential and Theoretical Physics. 130 (2020) 321-326. https://doi.org/10.1134/S1063776120020168.
[16] S. Floerchinger, C. Wetterich, Superfluid Bose gas in two dimensions, Phys. Rev. A, 79 (2009) 013601(1)-013601(9). https://doi.org/10.1103/PhysRevA.79.013601.
[17] J.O. Andersen, Theory of the weakly interacting Bose gas, Rev. Mod. Phys. 76 (2004) 599-639. https://doi.org/10.1103/RevModPhys.76.599.
[18] Y.B. Ivanov, F. Riek, J. Knoll, Gapless Hartree-Fock resummation scheme for the O(N) model, Phys. Rev. D, 71 (2005) 105016(1)-105016(11). https://doi.org/10.1103/PhysRevD.71.105016.
[19] G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, San Diego: San Diego: Academic, 2005.
[20] F.A. van Abeelen, B.J. Verhaar, Determination of collisional properties of cold Na atoms from analysis of bound-state photoassociation and Feshbach resonance field data, Physical Review A. 59 (1999) 578-584. https://doi.org/10.1103/PhysRevA.59.578.
[21] S. Biswas, J.K. Bhattacharjee, D. Majumder, K. Saha, N. Chakravarty, Casimir force on an interacting Bose–Einstein condensate, Journal of Physics B. 43 (2010) 085305-085312. https://doi.org/10.1088/0953-4075/43/8/085305.
[22] S. Inouye, M.R. Andrews, J. Stenger, H.J. Miesner, D.M. Stamper-Kurn, W. Ketterle, Observation of Feshbach resonances in a Bose-Einstein condensate, Nature. 392 (1998) 151-154. https://doi.org/10.1038/32354.