Communications in Theoretical Physics

Functional Integral Approach to Transition Temperature of a Homogeneous Imperfect Bose Gas

Guangxi Hu, Xian-xi Dai, JiXin Dai, William Edwin Evenson

Published Jun 15, 2004• 0 citations

Abstract

A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.

DOI: 10.1088/0253-6102/41/6/895

Related papers

Functional Integral Approach to Transition Temperature of a Homogeneous ImperfectBose Gas

HUGuang-Xi, DAIXian-Xi, DAIJi-Xin

A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as △Tc/To = 2.492 (na3) 1/6, where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.

理论物理通讯：英文版Jan 1, 20040 citations

Functional Integral Approach to the Transition Temperature of Attractive Interacting Bose Gas in Traps

Guangxi Hu, Xianxi Dai

Chinese Physics LettersJul 1, 20041 citation

Transition temperature of the homogeneous imperfect Bose gas

Nguyễn Văn Thụ, Pham Duy Thanh

arXiv:2409.14036Sep 21, 20240 citations

Transition Temperature of a Uniform Imperfect Bose Gas

Kerson Huang

arXiv:cond-mat/9904027Physical Review LettersNov 8, 199972 citations

BEC Transition Temperature of a Dilute Homogeneous Imperfect Bose Gas

Peter B. Arnold, Guy D. Moore

arXiv:cond-mat/0103228Physical Review LettersAug 28, 2001197 citations

Transition temperature for weakly interacting homogeneous Bose gases

F. Cruz, Marcus Benghi Pinto, Rudnei O. Ramos

arXiv:cond-mat/0007151Physical review. B, Condensed matterJun 14, 200163 citations

Communications in Theoretical Physics

Functional Integral Approach to Transition Temperature of a Homogeneous Imperfect Bose Gas

Guangxi Hu, Xian-xi Dai, JiXin Dai, William Edwin Evenson

Published Jun 15, 2004• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/41/6/895

Related papers

Functional Integral Approach to Transition Temperature of a Homogeneous ImperfectBose Gas

HUGuang-Xi, DAIXian-Xi, DAIJi-Xin

A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as △Tc/To = 2.492 (na3) 1/6, where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.

理论物理通讯：英文版Jan 1, 20040 citations

Functional Integral Approach to the Transition Temperature of Attractive Interacting Bose Gas in Traps

Guangxi Hu, Xianxi Dai

The functional integral approach (FIA) is introduced to study the transition temperature of an imperfect Bose gas in traps. An interacting model in quantum statistical mechanics is presented. With the model we study a Bose gas with attractive interaction trapped in an external potential. We obtain the result that the transition temperature of a trapped Bose gas will slightly shift upwards owing to the attractive interacting force. Successful application of the FIA to Bose systems is demonstrated.The functional integral approach (FIA) is introduced to study the transition temperature of an imperfect Bose gas in traps. An interacting model in quantum statistical mechanics is presented. With the model we study a Bose gas with attractive interaction trapped in an external potential. We obtain the result that the transition temperature of a trapped Bose gas will slightly shift upwards owing to the attractive interacting force. Successful application of the FIA to Bose systems is demonstrated.

Chinese Physics LettersJul 1, 20041 citation

Transition temperature of the homogeneous imperfect Bose gas

Nguyễn Văn Thụ, Pham Duy Thanh

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.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.

arXiv:2409.14036Sep 21, 20240 citations

Transition Temperature of a Uniform Imperfect Bose Gas

Kerson Huang

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase ${K}_{0}({\mathrm{na}}^{3}{)}^{1/6}$ , where $n$ is the density, $a$ is the $S$ -wave scattering length, and ${K}_{0}$ is a constant given in the paper. This disagrees with all existing results, analytical or numerical.We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase ${K}_{0}({\mathrm{na}}^{3}{)}^{1/6}$, where $n$ is the density, $a$ is the $S$-wave scattering length, and ${K}_{0}$ is a constant given in the paper. This disagrees with all existing results, analytical or numerical.

arXiv:cond-mat/9904027Physical Review LettersNov 8, 199972 citations

BEC Transition Temperature of a Dilute Homogeneous Imperfect Bose Gas

Peter B. Arnold, Guy D. Moore

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount $\ensuremath{\Delta}{T}_{c}\ensuremath{\simeq}{\mathrm{ca}}_{\mathrm{sc}}{n}^{1/3}{T}_{0}$ from the ideal gas result ${T}_{0}$ , 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 $c\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.32\ifmmode\pm\else\textpm\fi{}0.02$.The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount $\ensuremath{\Delta}{T}_{c}\ensuremath{\simeq}{\mathrm{ca}}_{\mathrm{sc}}{n}^{1/3}{T}_{0}$ from the ideal gas result ${T}_{0}$, 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 $c\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.32\ifmmode\pm\else\textpm\fi{}0.02$.

arXiv:cond-mat/0103228Physical Review LettersAug 28, 2001197 citations

Transition temperature for weakly interacting homogeneous Bose gases

F. Cruz, Marcus Benghi Pinto, Rudnei O. Ramos

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 $\ensuremath{\gamma}=3.059.$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 $\ensuremath{\gamma}=3.059.$

arXiv:cond-mat/0007151Physical review. B, Condensed matterJun 14, 200163 citations

{K}_{0}({\mathrm{na}}^{3}{)}^{1/6}

, where

n

is the density,

a

is the

S

-wave scattering length, and

{K}_{0}

is a constant given in the paper. This disagrees with all existing results, analytical or numerical.

{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 $\ensuremath{\gamma}=3.059.$