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. -> infinity while keeping the density rho=N/L(3) fixed and small. We prove a new lower bound for its ground state energy per particle, E(N, Lambda) /N >= 4 pi a rho[1 - O(rho(1/3)vertical bar log rho vertical bar(3))], as rho -> 0, where a is the scattering length of V. (C) 2010 American Institute of Physics. [doi:10.1063/1.3376639]