Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of $\sqrt{ρa^3}$ , where $ρ$ is the number density and $a$ is the S-wave scattering length. We calculate the ground state energy density to second order in $\sqrt{ρa^3}$ . The coefficient of the $ρa^3$ correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on $a$ , but also on an extra parameter that describes the low energy $3\to 3$ scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is $ρa \ell_V^2$ , and $\ell_V$ is the length scale set by the van der Waals potential.Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of $\sqrt{ρa^3}$, where $ρ$ is the number density and $a$ is the S-wave scattering length. We calculate the ground state energy density to second order in $\sqrt{ρa^3}$. The coefficient of the $ρa^3$ correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on $a$, but also on an extra parameter that describes the low energy $3\to 3$ scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is $ρa \ell_V^2$, and $\ell_V$ is the length scale set by the van der Waals potential.

arXiv:cond-mat/9712041Dec 3, 19971 citation

Binding energy of homogeneous Bose gases

Phan Thành Nam

arXiv:1703.10989Letters in Mathematical PhysicsSep 7, 20178 citations

Ground State Energy of the Low Density Bose Gas

Elliolt H. Lieb, Jakob Yngvason

Springer eBooksFeb 8, 2006106 citations

Ground-state properties of a trapped Bose gas beyond the mean-field approximation

Arup Banerjee, Manoranjan P. Singh

We study the effect of interatomic correlations beyond the mean-field approximation on the ground-state properties of a trapped Bose gas interacting through a repulsive potential. To this end we employ a variational procedure that is based on the energy functional derived, in the local-density approximation, using the low-density expansion for the ground-state energy of the homogeneous gas. We also make analytic estimates of the corrections due to the higher-order terms in the expansion. We find that corrections are of the order of $1%.$ However, there is a qualitative change in the density profile for large N (number of atoms) due to presence of a logarithmic term in the expansion.We study the effect of interatomic correlations beyond the mean-field approximation on the ground-state properties of a trapped Bose gas interacting through a repulsive potential. To this end we employ a variational procedure that is based on the energy functional derived, in the local-density approximation, using the low-density expansion for the ground-state energy of the homogeneous gas. We also make analytic estimates of the corrections due to the higher-order terms in the expansion. We find that corrections are of the order of $1%.$ However, there is a qualitative change in the density profile for large N (number of atoms) due to presence of a logarithmic term in the expansion.

Physical Review ANov 9, 200123 citations

Quantum corrections to the properties of a homogeneous interacting Bose gas at zero temperature can be calculated as a low-density expansion in powers of

\sqrt{ρa^3}

, where

ρ

is the number density and

a

is the S-wave scattering length. We calculate the ground state energy density to second order in

\sqrt{ρa^3}

. The coefficient of the

ρa^3

correction has a logarithmic term that was calculated in 1959. We present the first calculation of the constant under the logarithm. The constant depends not only on

a

, but also on an extra parameter that describes the low energy

3\to 3

scattering of the bosons. In the case of alkali atoms, we argue that the second order quantum correction is dominated by the logarithmic term, where the argument of the logarithm is

ρa \ell_V^2

, and

\ell_V

is the length scale set by the van der Waals potential.

1%.

However, there is a qualitative change in the density profile for large N (number of atoms) due to presence of a logarithmic term in the expansion.