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Europhysics Letters (EPL)

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

Phạm Thế Song

Published Jul 22, 2022• 6 citations
Publisher

Abstract

Abstract Based on the Cornwall-Jackiw-Tomboulis (CJT) effective action approach and the requirement to preserve the Goldstone theorem within two-loop approximation, we study the universal quantum effect, which is related to the two-body correlation, in a homogeneous weakly interacting Bose gas at zero temperature. We find the state equations that provide the condensate fraction, energy density, chemical potential, and sound speed. They are the series expansions of the gas parameter.

DOI
10.1209/0295-5075/ac8370

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By means of Cornwall-Jackiw-Tomboulis effective action approach we investigate a homogeneous dilute weakly interacting Bose gas at finite temperature in vicinity of critical region. A longstanding debate, the shift of critical temperature, is considered and obtained in the universal form ΔTC/TC(0)=cn01/3asΔT_C/T_C^{(0)} = cn_0^{1/3}a_sΔTC​/TC(0)​=cn01/3​as​ with constants ccc and aaa. The non-condensate fraction is contributed by quantum fluctuations as well as thermal exitations and can be expressed in sum of three terms. These terms correspond to the quantum fluctuations, thermal fluctuations and both. Indeed, the specific heat capacity and critical exponents are calculated and in excellent agreement with those in previous works and experimental data.
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Beyond standard approaches in existing literature, we explore the relative shift in the transition temperature of a homogeneous dilute Bose gas using the Cornwall-Jackiw-Tomboulis effective action formalism within the improved Hartree-Fock approximation. The first correction to the enhancement of the transition temperature, as compared to that of the ideal Bose gas, is expressed in a universal form: it is linear with respect to the scattering length. The slope of this linear relationship shows excellent agreement with the exact numerical calculations presented in previous studies. Additionally, we identify non-universal terms contributing to the shift.