Critical Temperature of Bose-Einstein condensation of hard sphere gases

Franck Laloë, David M. Ceperley, P. Grüter

Published Jan 1, 1997• 0 citations

Abstract

We determine the critical temperature of hard-sphere Bosons in a cubic box by path-integral Monte Carlo simulations and finite-size scaling. We obtain an enhancement compared to the ideal gas at low densities in the form of a power law in density with exponent $1/3$. At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior.

Related papers

Critical Temperature of Bose-Einstein Condensation of Hard-Sphere Gases

P. Grüter, David M. Ceperley, Franck Laloë

arXiv:cond-mat/9707028Physical Review LettersNov 10, 1997171 citations

Critical temperature of trapped hard-sphere Bose gases

Sean Pearson, Tao Pang, Changfeng Chen

Physical Review ADec 1, 199812 citations

Bose condensation in dilute gas of hard spheres with attraction

Sergey Ya. Bronin, B. V. Zelener, A. B. Klyarfeld +1 more

\n\nCritical temperature is calculated for Bose-Einstein condensation of hard spheres with attraction using the path-integral Monte Carlo (PIMC) method and finite-size scaling. It is demonstrated that the scattering length is not the only parameter which the critical temperature depends on. It is also shown that Bose condensation may be observed in the case of negative scattering length.\n

Europhysics Letters (EPL)Sep 1, 20134 citations

Bose-Einstein Condensation of Hard Sphere Homogeneous Gas in Static Fluctuation Approximation

Mohamed K. Al-Sugheir, S.S. Gasymeh, M. Shatnawi +1 more

The condensation fraction, transition temperature, and energy per particle for a hard sphere interacting homogeneous Bose gas using the static fluctuation approximation have been determined.The transition temperature at liquid helium density has been found to be lower than that for the noninteracting gas.Both superfluidity and the Bose-Einstein condensation have been found to occur at the same transition temperature.Our results are consistent with results obtained by other methods.

Acta Physica Polonica AAug 1, 20091 citation

Comment on ``Critical temperature of trapped hard-sphere Bose gases''

Werner Krauth

In this comment, I discuss a recent path-integral Monte Carlo calculation by Pearson, Pang, and Chen (Phys. Rev. A 58, 4796 (1998)). For bosons with a small hard-core interaction in a harmonic trap, the authors find a critical temperature which does not change with respect to the non-interacting gas. The calculation suffers from a serious discretization error of the many-particle density matrix.

arXiv:cond-mat/9812328Dec 19, 19980 citations

Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas: Path integral Monte Carlo study

Kwangsik T. Nho, David Paul Landau

arXiv:cond-mat/0404238Physical Review ANov 18, 200456 citations

Critical Temperature of Bose-Einstein condensation of hard sphere gases

Franck Laloë, David M. Ceperley, P. Grüter

Published Jan 1, 1997• 0 citations

OpenAlex

Abstract

1/3

. At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior.

Related papers

Critical Temperature of Bose-Einstein Condensation of Hard-Sphere Gases

P. Grüter, David M. Ceperley, Franck Laloë

We determine the critical temperature of a 3D homogeneous system of hard-sphere bosons by path-integral Monte Carlo simulations and finite-size scaling. In the low density limit, we find that the critical temperature is increased by the repulsive interactions, as $\ensuremath{\Delta}{T}_{C}{/T}_{0}\ensuremath{\sim}({\mathrm{na}}^{3}{)}^{\ensuremath{\gamma}}$, where $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.34\ifmmode\pm\else\textpm\fi{}0.03$. At high densities the result for liquid helium, namely, a lower critical temperature than in the noninteracting case, is recovered. We give a microscopic explanation for the observed behavior.We determine the critical temperature of a 3D homogeneous system of hard-sphere bosons by path-integral Monte Carlo simulations and finite-size scaling. In the low density limit, we find that the critical temperature is increased by the repulsive interactions, as $\ensuremath{\Delta}{T}_{C}{/T}_{0}\ensuremath{\sim}({\mathrm{na}}^{3}{)}^{\ensuremath{\gamma}}$, where $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.34\ifmmode\pm\else\textpm\fi{}0.03$. At high densities the result for liquid helium, namely, a lower critical temperature than in the noninteracting case, is recovered. We give a microscopic explanation for the observed behavior.

arXiv:cond-mat/9707028Physical Review LettersNov 10, 1997171 citations

Critical temperature of trapped hard-sphere Bose gases

Sean Pearson, Tao Pang, Changfeng Chen

We determine the critical temperature of parabolically trapped hard-sphere bosons via path-integral quantum Monte Carlo calculations of the condensate fraction and the specific heat. Contrary to previous predictions, the critical temperature of the weakly interacting gas remains roughly constant with respect to increases in the hard-sphere diameter, and is approximately equal to the critical temperature for ideal bosons. As the hard-sphere diameter is increased further, the critical temperature eventually begins to decrease. We give an explanation for the discrepancy between previous results and those presented here.We determine the critical temperature of parabolically trapped hard-sphere bosons via path-integral quantum Monte Carlo calculations of the condensate fraction and the specific heat. Contrary to previous predictions, the critical temperature of the weakly interacting gas remains roughly constant with respect to increases in the hard-sphere diameter, and is approximately equal to the critical temperature for ideal bosons. As the hard-sphere diameter is increased further, the critical temperature eventually begins to decrease. We give an explanation for the discrepancy between previous results and those presented here.

Physical Review ADec 1, 199812 citations

Bose condensation in dilute gas of hard spheres with attraction

Sergey Ya. Bronin, B. V. Zelener, A. B. Klyarfeld +1 more

Europhysics Letters (EPL)Sep 1, 20134 citations

Bose-Einstein Condensation of Hard Sphere Homogeneous Gas in Static Fluctuation Approximation

Mohamed K. Al-Sugheir, S.S. Gasymeh, M. Shatnawi +1 more

Acta Physica Polonica AAug 1, 20091 citation

Comment on ``Critical temperature of trapped hard-sphere Bose gases''

Werner Krauth

arXiv:cond-mat/9812328Dec 19, 19980 citations

Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas: Path integral Monte Carlo study

Kwangsik T. Nho, David Paul Landau

Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression ${T}_{c}={T}_{c}^{0}{1+{c}_{1}a{n}^{1∕3}+[{c}_{2}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(a{n}^{1∕3})+{c}_{2}^{\ensuremath{''}}]{a}^{2}{n}^{2∕3}+\mathrm{O}({a}^{3}n)}$, where ${T}_{c}^{0}$ 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.Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression ${T}_{c}={T}_{c}^{0}{1+{c}_{1}a{n}^{1∕3}+[{c}_{2}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(a{n}^{1∕3})+{c}_{2}^{\ensuremath{''}}]{a}^{2}{n}^{2∕3}+\mathrm{O}({a}^{3}n)}$, where ${T}_{c}^{0}$ 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.

arXiv:cond-mat/0404238Physical Review ANov 18, 200456 citations

1/3

. At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior.

{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.