Ground-State Energy and Condensate Density of a Dilute Bose Gas Revisited

Abstract

The ground-state energy per particle $E/N$ and condensate density $n_0$ of a dilute Bose gas are studied with a self-consistent perturbation expansion satisfying the Hugenholtz-Pines theorem and conservation laws simultaneously. A class of Feynman diagrams for the self-energy, which has escaped consideration so far, is shown to add an extra constant $c_{ip}\sim O(1)$ to the expressions reported by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957) ] as $E/N=(2\pi {\hslash }^{2}an/m)[1+(128/15\sqrt{\pi }+16c_{ip}/5)\sqrt{a^{3}n}]$ and $n_0/n=1-(8/3\sqrt{\pi }+c_{ip})\sqrt{a^{3}n}$, where $a$, $n$, and $m$ are are the s-wave scattering length, particle density, and particle mass, respectively. We present a couple of estimates for $c_{ip}$; the third-order perturbation expansion yields $c_{ip}=0.412$.

5 pages, 3 figures

References in corpus (4)

• Dynamics and Thermodynamics of the Low-Temperature Strongly Interacting Bose Gas
• Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws
• Exact results on the two-particle Green's function of a Bose-Einstein condensate
• Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate

Cited by in corpus (3)

• Effective action for Bose-Einstein condensates
• Universal and Non-Universal Correction Terms of Bose Gases in Dilute Region: a Quantum Monte Carlo Study
• Lifetime of Single-Particle Excitations in a Dilute Bose-Einstein Condensate at Zero Temperature