理论物理通讯：英文版

Functional Integral Approach to Transition Temperature of a Homogeneous ImperfectBose Gas

HUGuang-Xi, DAIXian-Xi, DAIJi-Xin

Published Jan 1, 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 △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.

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

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理论物理通讯：英文版

Functional Integral Approach to Transition Temperature of a Homogeneous ImperfectBose Gas

HUGuang-Xi, DAIXian-Xi, DAIJi-Xin

Published Jan 1, 2004• 0 citations

OpenAlex

Abstract

Related papers

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

Guangxi Hu, Xian-xi Dai, JiXin Dai +1 more

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.

Communications in Theoretical PhysicsJun 15, 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.

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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

{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_c-T_c^0)/T_c^0 = -0.93 aρ^{1/3}

, where T_c^0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and

ρ

is the particle number density.

{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 $c\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.32\ifmmode\pm\else\textpm\fi{}0.02$.