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

26 pages, AMS LaTex

References in corpus (5)

• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• Ground State Energy of the Two-Component Charged Bose Gas
• The ground state energy of the weakly interacting Bose gas at high density
• One-Dimensional Behavior of Dilute, Trapped Bose Gases
• The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

Cited by in corpus (3)

• On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
• Free Energies of Dilute Bose gases: upper bound
• Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional