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

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

2009-08-02

arxiv.org/abs/0908.0109v2

J. Math. Phys. 51, 053302 (2010)

Physics

Mathematical Physics

26 pages, AMS LaTex

Scientific paper

10.1063/1.3376639

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 $$\frac{E(N, \Lambda)}{N} \geq 4 \pi a \rho [ 1 - O(\rho^{1/3} |\log \rho|^3) ],$$ as $\rho \to 0$, where $a$ is the scattering length of $V$.

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