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

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Abstract

The leading term of the ground state energy/particle of a dilute gas of bosons with mass m in the thermodynamic limit is \({2\pi \hbar^2 a \varrho/m}\) when the density of the gas is \({\varrho}\), 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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Correspondence to Jun Yin.

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Communicated by H.-T. Yau

©2009 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes.

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Yin, J. The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length. Commun. Math. Phys. 295, 1–27 (2010). https://doi.org/10.1007/s00220-009-0977-z

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  • DOI: https://doi.org/10.1007/s00220-009-0977-z

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