Ground State Energy of Dilute Bose Gas in Small Negative Potential Case

Details Ground State Energy of Dilute Bose Gas in Small Negative Potential Case Ground State Energy of Dilute Bose Gas in Small Negative Potential Case

2008-03-04

arxiv.org/abs/0803.0533v3

J. Stat. Phys. (2009) 134:1-18

Physics

Mathematical Physics

13 pages, AMS-LaTeX

Scientific paper

It is well known that the ground state energy of a three dimensional dilute Bose gas in the thermodynamic limit is $E=4\pi a \rho N$ when the particles interact via a non-negative, finite range, symmetric, two-body potential. Here, $N$ is the number of particles, $\rho$ is the density of the gas, and $a$ is the scattering length of the potential. In this paper, we prove the same result without the non-negativity condition on the potential, provided the negative part is small.

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