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arXiv:1809.10930 · International Journal of Modern Physics B

Finite-size effect on Bose–Einstein condensate mixtures in improved Hartree–Fock approximation

Nguyễn Văn Thụ, Luong Thi Theu

Published Apr 29, 2019• 11 citations
arXivHTMLPDF

Abstract

By means of Cornwal–Jackiw–Tomboulis effective action approach we considered the finite-size effect on Bose–Einstein condensate mixtures confined between two parallel palates. Keeping upto double-bubble approximation and taking into account the conservation of Goldstone boson, our results are quite different from those in previous works within one-loop approximation. The order parameters strongly depend on the distance between palates and can be expressed via the correction terms. The Casimir force is also considered.

DOI
10.1142/s0217979219501145

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By means of Cornwal–Jackiw–Tomboulis effective action approach we considered the finite-size effect on Bose–Einstein condensate mixtures confined between two parallel palates. Keeping upto double-bubble approximation and taking into account the conservation of Goldstone boson, our results are quite different from those in previous works within one-loop approximation. The order parameters strongly depend on the distance between palates and can be expressed via the correction terms. The Casimir force is also considered.
Abstract By means of the Cornwall–Jackiw–Tomboulis effective potential formalism, the Casimir effect in binary Bose–Einstein condensate mixtures is investigated. The study conditions are that the mixtures are confined between two parallel plates at zero temperature and within the improved Hartree–Fock approximation featuring higher-order terms in the momentum integrals. Our results show that both effective masses and order parameters strongly depend on the distance between the two plates. The Casimir energy and resulting Casimir force are scrutinized, confirming that the contribution of the higher-order terms of the momentum integrals is significant. Importantly, the Casimir force is proved to be non-zero in limit of the full strong segregation, which is an acceptable answer for the controversial problem.
Abstract The density of condensates of a binary mixture of Bose gases restricted by two parallel planar walls is investigated within the framework of Cornwal-Jackiw-Tomboulis effective action approach in improved Hartree-Fock approximation. It results that the density of condensates strongly depend not only on the distance between two walls but also on the interspecies interaction strength and they are equal their expectation values of the field operators after adding a term associated with the quantum fluctuations.
We show various aspects of finite size effects on Bose-Einstein condensation(BEC). In the first section we introduce very briefly the BEC of harmonically trapped ideal Bose gas. In the second section we theoretically argued that Bose-Einstein(B-E) statistics needs a correction for finite system at ultralow temperatures. As a corrected statistics we introduced a Tsallis type of generalized B-E statistics. The condensate fraction calculated with this generalized B-E statistics, is satisfied well with the experimental result. In the third section we show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperatures. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached. Our results support the experimental result which was obtained well below the condensation temperature. In the fourth section we concentrate on the thermodynamic Casimir force on the Bose-Einstein condensate. We explored the temperature dependence of the Casimir force.