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 ({\Lambda}) of side length ({L}). We take the limit ({N}), ({L}) ({\rightarrow}) ({\infty}) while keeping the density ({\rho}) = ({N})/({L})({^3}) fixed and small. We prove a new lower bound for its ground state energy per particle $$\frac{E(N, \Lambda)}{N} \geq 4 \pi a \rho [ 1 - O(\rho^{1/3} |\log \rho|^3) ],$$ as ({\rho})({\rightarrow}) 0, where ({a}) is the scattering length of ({V}).