Elliott H. Lieb, Jakob Yngvason
The Ground State Energy of a Dilute Bose Gas
(40K, Latex2e)
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 $\rho$ is $2\pi\hbar^2\rho a/m$ to leading order in
$\rho a^3\ll 1$, 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.