The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

Details The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

2008-08-29

arxiv.org/abs/0808.4066v1

Com. Math. Phys. Vol 295, No.1 (2010) 1-27

Physics

Mathematical Physics

Latex 28 pages

Scientific paper

10.1007/s00220-009-0977-z

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2\pi \hbar^2 a \rho/m$ when the density of the gas is $\rho$, the interaction potential is non-negative and the scattering length $a$ is positive. In this paper, we generalize the upper bound part of this result to any interaction potential with positive scattering length, i.e, $a>0$ and the lower bound part to some interaction potentials with shallow and/or narrow negative parts.

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