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

Abstract

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2\pi {\hslash }^{2}a\rho /m$ 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.

Latex 28 pages

References in corpus (4)

• Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The ground state energy of a low density Bose gas: a second order upper bound
• Ground State Energy of the Low Density Fermi Gas

Cited by in corpus (7)

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• Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional
• Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
• A Lower Bound on the Ground State Energy of Dilute Bose Gas
• Ground State Energy of Dilute Bose Gas in Small Negative Potential Case