The finite size effect causes many interesting behaviors in properties of a weakly interacting Bose gas. These behaviors were considered in one-loop approximation of quantum field theory. In this paper the influence is investigated in improved Hatree-Fock approximation, which gives more accurate results. | VNU Journal of Science: Mathematics – Physics, Vol. 34, No. 3 (2018) 43-47 Influence of the Finite Size Effect on Properties of a Weakly Interacting Bose G as in Improved Hatree-fock Approximation Nguyen Van Thu*, Luong Thi Theu Department of Physics, Hanoi Pedagogical University 2, Nguyen Van Linh, Phuc Yen, Vinh Phuc, Vietnam Received 28 July 2018 Revised 11 August 2018; Accepted 11 August 2018 Abstract: The finite size effect causes many interesting behaviors in properties of a weakly interacting Bose gas. These behaviors were considered in one-loop approximation of quantum field theory. In this paper the influence is investigated in improved Hatree-Fock approximation, which gives more accurate results. Keywords: Finite size effect, improved Hatree-Fock approximation, Bose-Einstein condensate. 1. Introduction The finite size effect is one of the most interesting effects in quantum physics, which takes place in all of real systems and has been considered thoroughly. It is a hot topic in magnetic material [1], superconductivity [2], nuclear matter [3] and so on. In Bose-Einstein condensate (BEC) field, the finite size effect causes the quantum fluctuation on top of the ground state, which leads to Casimir effect [4]. For two-component Bose-Einstein condensates, this effect was investigated in [5], in which two essential results are that the Casimir force is not simple superposition of the one of two single component BEC due to the interaction between two species and one of the most important result is that this force is vanishing in limit of strong segregation. In a dilute BEC, using Euler–Maclaurin formula, author of Ref. [6] calculated the Casimir force corresponding to Dirichlet and Robin boundary conditions. The result shows that the Casimir force is attractive and divergent when distance between two slabs approaches to zero. One common thing of these papers is that the finite size effect is studied in one-loop approximation. In this respect, the effective
