arXiv:cond-mat/9904027 · Physical Review Letters

Transition Temperature of a Uniform Imperfect Bose Gas

Kerson Huang

Published Nov 8, 1999• 72 citations

Abstract

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.

DOI: 10.1103/physrevlett.83.3770

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

The Transition Temperature of the Dilute Interacting Bose Gas

Gordon Baym, Jean-Paul Blaizot, Markus Holzmann +2 more

arXiv:cond-mat/9905430Physical Review LettersAug 30, 1999248 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

Equation of state of an interacting Bose gas at finite temperature: A path-integral Monte Carlo study

Sebastiano Pilati, K. Sakkos, Jordi Boronat +2 more

arXiv:cond-mat/0607721Physical Review AOct 27, 200629 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

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

arXiv:cond-mat/9904027 · Physical Review Letters

Transition Temperature of a Uniform Imperfect Bose Gas

Kerson Huang

Published Nov 8, 1999• 72 citations

arXiv HTML PDF

Abstract

{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.

DOI: 10.1103/physrevlett.83.3770

Related papers

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

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

Communications in Theoretical PhysicsJun 15, 20040 citations

The Transition Temperature of the Dilute Interacting Bose Gas

Gordon Baym, Jean-Paul Blaizot, Markus Holzmann +2 more

We show that the critical temperature of a uniform dilute Bose gas increases linearly with the $s$ -wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.We show that the critical temperature of a uniform dilute Bose gas increases linearly with the $s$-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

arXiv:cond-mat/9905430Physical Review LettersAug 30, 1999248 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

Equation of state of an interacting Bose gas at finite temperature: A path-integral Monte Carlo study

Sebastiano Pilati, K. Sakkos, Jordi Boronat +2 more

By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same $s$ -wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.By using exact path-integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same $s$-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.

arXiv:cond-mat/0607721Physical Review AOct 27, 200629 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

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

{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 show that the critical temperature of a uniform dilute Bose gas increases linearly with the

s

-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

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 $\ensuremath{\gamma}=3.059.$

s

-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.

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