arXiv:2409.14036

Transition temperature of the homogeneous imperfect Bose gas

Nguyễn Văn Thụ, Pham Duy Thanh

Published Sep 21, 2024• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.2409.14036

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arXiv:2409.14036

Transition temperature of the homogeneous imperfect Bose gas

Nguyễn Văn Thụ, Pham Duy Thanh

Published Sep 21, 2024• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.2409.14036

Related papers

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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.

{T}_{0}

, where

{a}_{\mathrm{sc}}

is the scattering length,

n

is the density, and

c

is a pure number. There have been several different theoretical estimates for

c

. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) ${\ensuremath{\varphi}}^{4}$ field theory in three dimensions---an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce nonuniversal quantities such as the critical temperature. We find $c\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.32\ifmmode\pm\else\textpm\fi{}0.02$.

We apply the nonperturbative optimized linear $\ensuremath{\delta}$ expansion method to the

O(N)

scalar field model in three dimensions to determine the transition temperature of a dilute homogeneous Bose gas. Our results show that the shift of the transition temperature $\ensuremath{\Delta}{T}_{c}{/T}_{c}$ of the interacting model, compared with the ideal-gas transition temperature, really behaves as $\ensuremath{\gamma}{\mathrm{an}}^{1/3}$ where a is the s-wave scattering length and n is the number density. For

N=2

our calculations yield the value $\ensuremath{\gamma}=3.059.$