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Ground state property of Bose-Einstein gas for arbitrary power low interaction

Makoto Hiramoto
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Abstract

We study Bose-Einstein gas for an arbitrary power low interaction $C_αr^{-α}$. This is done by the Hartree Fock Bogoliubov (HFB) approach at $T \le T_{c}$ and the mean field approach at $T>T_{c}$. Especially, we investigate the ground state property of Bose gas interacting through the Van der Waals $-C_{6}r^{-6}$ plus $C_{3}r^{-3}$ interactions. We show that the ground state under this interaction is stable if the ratio of coupling constants is larger than that of the critical curve. We find that the $C_{3}r^{-3}$ term plays an important role for the stability of the ground state when the density of atoms becomes sufficiently large at low temperature. Further, using the numerical values of $C_{3}$ and $C_{6}$, we confirm that the ground state of alkali atoms are stable.

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Makoto Hiramoto. 2002-01-16. Ground state property of Bose-Einstein gas for arbitrary power low interaction. https://arxiv.org/abs/cond-mat/0201265

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