A Lower Bound on the Ground State Energy of Dilute Bose Gas

Abstract

Consider an N-Boson system interacting via a two-body repulsive short-range potential $V$ in a three dimensional box $Λ$ of side length $L$. We take the limit $N, L \to \infty$ while keeping the density $ρ= N / L^3$ fixed and small. We prove a new lower bound for its ground state energy per particle $$\frac{E(N, Λ)}{N} \geq 4 πa ρ[ 1 - O(ρ^{1/3} |\log ρ|^3) ],$$ as $ρ\to 0$, where $a$ is the scattering length of $V$.

26 pages, AMS LaTex