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The Ground State Energy of a Dilute Bose Gas

Elliott H. Lieb·Jakob Yngvason
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Abstract

According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density $ρ$ is $2π\hbar^2ρa/m$ to leading order in $ρa^3\ll 1$, where $a$ is the scattering length of the interaction potential and $m$ the particle mass. This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the first time. We give here an account of the proof that applies to nonnegative, spherically symmetric potentials decreasing faster than $1/r^3$ at infinity.

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Elliott H. Lieb, Jakob Yngvason. 2000-08-20. The Ground State Energy of a Dilute Bose Gas. https://arxiv.org/abs/math-ph/9910033

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