The Repulsive Casimir-Type Forces of a Weakly Interacting Bose–Einstein Condensate Gas

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

“…, 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…”

“…When the fluctuation fields φ 1 and φ 2 , which represent the excitation atomic state, are not considered, hence P 11 = P 22 = 0, and the chemical potential is approximated as μ = λφ 2 0 /2 [4,43], eqs. ( 5), ( 7) and ( 8) turn into the potential density, inversion propagator, and dispersion relation within oneloop approximation as [42,47]…”