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VNU Journal of Science Mathematics - Physics

Condensate Density of a Bose Gas Confined between Two Parallel Plates in Canonical Ensemble within Improved Hartree-Fock Approximation

Nguyễn Văn Thụ

Published Oct 7, 2020• 0 citations
Publisher

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.

DOI
10.25073/2588-1124/vnumap.4502

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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.
In a manner of Cornwal-Jackiw-Tomboulis effective action approach, the density of condensate of a dilute Bose gas confined between two planar walls is investigated within the framework of improved Hartree-Fock. Thereby, the quantum fluctuations are taken into account with presence of high-order terms in the momentum integrals. Our results show that the quantum fluctuations significantly belittle the density of condensate compared with square of the expectation value of the field operator. The comparison with relating results of Gross-Pitaevskii theory is made.
In a manner of Cornwal-Jackiw-Tomboulis effective action approach, the density of condensate of a dilute Bose gas confined between two planar walls is investigated within the framework of improved Hartree-Fock. Thereby, the quantum fluctuations are taken into account with presence of high-order terms in the momentum integrals. Our results show that the quantum fluctuations significantly belittle the density of condensate compared with square of the expectation value of the field operator. The comparison with relating results of Gross-Pitaevskii theory is made.
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.
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.