Ground State Energy of the Low Density Bose Gas

TL;DR

This paper rigorously establishes the correct lower bound for the ground state energy of a low density Bose gas, confirming the long-standing formula for the leading energy term per particle.

Contribution

The paper provides the first rigorous proof of the lower bound for the ground state energy of a low density Bose gas, validating the formula involving scattering length.

Findings

Established the correct lower bound for the energy.

Confirmed the leading term in energy per particle as 2πħ²ρa/m.

Resolved a 40-year-old open problem in Bose gas theory.

Abstract

Now that the properties of low temperature Bose gases at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4-5 decades ago. One of these is that the leading term in the energy/particle is $2\pi \hbar^2 \rho a/m$, where $a$ is the scattering length. Owing to the delicate and peculiar nature of bosonic correlations, four decades of research have failed to establish this plausible formula rigorously. The only known lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct bound is proved here.