Journal of Eastchina Normal University

Condensation Temperature of Uniform Interacting Bose Gases

Shu Liu

Published Jan 1, 2001• 0 citations

Abstract

The Bose-Einstein condensation (BEC) of weakly interacting Bose gases has been realized recently in experiment. The condensation temperature of a uniform interacting Bose gas is an important thermodynamic quantity fot the BEC. In this paper, the pseudopotential method and grand canonical ensemble are used to investigate the condensation temperature of the uniform interacting Bose gas. The results show that, due to the interaction between particles, the shift of the condensation temperature is δT c/T c=-2.9an 1/3 , where a and n are the two-particle scattering length of S- wave and the particle number density, respectively.

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Journal of Eastchina Normal University

Condensation Temperature of Uniform Interacting Bose Gases

Shu Liu

Published Jan 1, 2001• 0 citations

OpenAlex

Abstract

Related papers

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Boris Kastening

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length $a$ is computed for given particle density $n$ . Variational perturbation theory is used to resum the corresponding perturbative series for $\ensuremath{\Delta}⟨{\ensuremath{\phi}}^{2}⟩∕Nu$ in a classical three-dimensional scalar field theory with coupling $u$ and where the physical case of $N=2$ field components is generalized to arbitrary $N$ . Our results for $N=1,2,4$ are in agreement with recent Monte Carlo simulations; for $N=2$ , we obtain $\ensuremath{\Delta}{T}_{c}∕{T}_{0}=(1.27\ifmmode\pm\else\textpm\fi{}0.11)a{n}^{1∕3}$. We use seven-loop perturbative coefficients, extending earlier work by one loop order.The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length $a$ is computed for given particle density $n$. Variational perturbation theory is used to resum the corresponding perturbative series for $\ensuremath{\Delta}⟨{\ensuremath{\phi}}^{2}⟩∕Nu$ in a classical three-dimensional scalar field theory with coupling $u$ and where the physical case of $N=2$ field components is generalized to arbitrary $N$. Our results for $N=1,2,4$ are in agreement with recent Monte Carlo simulations; for $N=2$, we obtain $\ensuremath{\Delta}{T}_{c}∕{T}_{0}=(1.27\ifmmode\pm\else\textpm\fi{}0.11)a{n}^{1∕3}$. We use seven-loop perturbative coefficients, extending earlier work by one loop order.

arXiv:cond-mat/0309060Physical Review AApr 21, 200494 citations

n

is the density and

a

is the

S

-wave scattering length.

(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}_{c}^{0}

is the critical temperature for an ideal gas,

a

is the

s

-wave scattering length, and

n

is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient

{c}_{1}

between their results and the (apparently) other reliable results in the literature. Our results show that ${({T}_{c}\ensuremath{-}{T}_{c}^{0})∕{T}_{c}^{0}}∕(a{n}^{1∕3})$ depends strongly on the interaction strength

a{n}^{1∕3}

while the previous PIMC results are considerably flatter and smaller than our results. We obtain ${c}_{1}=1.32\ifmmode\pm\else\textpm\fi{}0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\ensuremath{\phi}}^{4}$ field theory and variational perturbation theory.

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length

a

is computed for given particle density

n

. Variational perturbation theory is used to resum the corresponding perturbative series for $\ensuremath{\Delta}⟨{\ensuremath{\phi}}^{2}⟩∕Nu$ in a classical three-dimensional scalar field theory with coupling

u

and where the physical case of

N=2

field components is generalized to arbitrary

N

. Our results for

N=1,2,4

are in agreement with recent Monte Carlo simulations; for

N=2

, we obtain $\ensuremath{\Delta}{T}_{c}∕{T}_{0}=(1.27\ifmmode\pm\else\textpm\fi{}0.11)a{n}^{1∕3}$. We use seven-loop perturbative coefficients, extending earlier work by one loop order.