The Condensed Fraction of a Homogeneous Dilute Bose Gas Within the Improved Hartree–Fock Approximation

Abstract

By means of Cornwall-Jackiw-Tomboulis effective action we investigate a dilute weakly interacting Bose gas at finite temperature. The shift of critical temperature is obtained in the universal form ∆T C /T (0) C = c.n 1/3 0 a s with constant c. The non-condensate fraction is expressed in sum od three terms, which correspond to the quantum fluctuation, thermal fluctuation and both.

Universal quantum effect of two-body correlation in a weakly interacting Bose gas

“…The obvious difference between the excitation atomic density equation (38), the chemical potential equation (41), and the quantum energy density equation (45) with the ones in ref. [45] is the replacement of ρ c by ρ. The other differences also appear in the coefficients of the higherorder series expansion of the gas parameter, such as comparing the third term of the above equation ( 45) with the corresponding one in ref.…”

“…( 41) by taking the first derivative of the energy density equation (45) regarding the atomic density. The obvious difference between the excitation atomic density equation (38), the chemical potential equation (41), and the quantum energy density equation (45) with the ones in ref. [45] is the replacement of ρ c by ρ.…”

“…The other differences also appear in the coefficients of the higherorder series expansion of the gas parameter, such as comparing the third term of the above equation ( 45) with the corresponding one in ref. [45]. To find the effective mass, the chemical potential in ref.…”

“…, respectively, being the inversion propagators within one-loop approximation [42,43] and two-loop approximation [44,45]. The notation β represents the combining the sum over the bosonic Matsubara frequencies with the integral in momentum space as…”

“…As pointed out in refs. [44,45], the effective potential equation ( 5) and inversion propagator equation (7) give the dispersion relation…”