Casimir force of a dilute Bose gas confined by a parallel plate geometry in improved Hatree-Fock approximation

TL;DR

This paper investigates the Casimir force in a dilute Bose-Einstein condensate confined between parallel plates using the improved Hartree-Fock approximation, highlighting the effects of higher-order corrections.

Contribution

It introduces a detailed analysis of the Casimir force in BECs within the IHF approximation, including two-loop diagram contributions, and compares it to the one-loop approximation.

Findings

Effective mass and order parameter depend strongly on plate separation.

Casimir force in IHF is the sum of one-loop results plus two-loop corrections.

One-loop approximation suffices for ideal Bose gas Casimir calculations.

Abstract

Within framework of quantum field theory, in improved Hatree-Fock (IHF) approximation, we have considered a dilute single Bose-Einstein condensate (BEC) confined between two parallel plates. We found that the effective mass and order parameter of BEC strongly depend on distance separating two plates. Our results shows that the effective mass, order parameter and the Casimir force in IHF approximation equal to their values in one-loop approximation added a corrected term due to contribution of two-loop diagrams. We also show that the one-loop approximation is enough for calculating Casimir effect in an ideal Bose gas.