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arXiv:2311.13822

Critical temperature and thermodynamic properties of a homogeneous dilute weakly interacting Bose gas within the improved Hartree-Fock approximation at finite temperature

Nguyễn Văn Thụ, Thanh, Pham Duy

Published Nov 23, 2023• 0 citations
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Abstract

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 $ΔT_C/T_C^{(0)} = cn_0^{1/3}a_s$ with constants $c$ and $a$. 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.

DOI
10.48550/arxiv.2311.13822

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This article reviews recent advances in the theory of the three-dimensional dilute homogeneous Bose gas at zero and finite temperature. Effective-field-theory methods are used to formulate a systematic perturbative framework that can be used to calculate the properties of a system at T=0.T=0.T=0. The perturbative expansion of these properties is essentially an expansion in the gas parameter na3,\sqrt{{\mathrm{na}}^{3}},na3​, where aaa is the sss-wave scattering length and nnn is the number density. In particular, the leading quantum corrections to the ground-state energy density, the condensate depletion, and long-wavelength collective excitations are rederived in an efficient and economical manner. Nonuniversal effects are also discussed. These effects are higher-order corrections that depend on properties of the interatomic potential other than the scattering length, such as the effective range. The article critically examines various approaches to the dilute Bose gas in equilibrium at finite temperature. These include the Bogoliubov approximation, the Popov approximation, the Hartree-Fock-Bogoliubov approximation, the \ensuremath{\Phi}-derivable approach, optimized perturbation theory, and renormalization-group techniques. The article ends with a look at recent calculations of the critical temperature of the dilute Bose gas, which include 1/N1/N1/N techniques, lattice simulations, self-consistent calculations, and variational perturbation theory.