### Abstract

The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E_{0}/N = (2πh^{2}p/m) |1n(pa^{2})| ^{-1}, to leading order, with a relative error at most O(|1n(pa^{2})|^{-1/5}). Here N is the number of particles, p = N/V is the particle density and a is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, E_{0} is not simply N(N-1)/2 times the energy of two particles in a large box of volume (area, really) V. It is much larger.

Original language | English (US) |
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Pages (from-to) | 509-526 |

Number of pages | 18 |

Journal | Journal of Statistical Physics |

Volume | 103 |

Issue number | 3-4 |

DOIs | |

State | Published - May 1 2001 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

- Bose gas
- Ground state energy
- Low density
- Scattering length
- Two-dimensions

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## Cite this

*Journal of Statistical Physics*,

*103*(3-4), 509-526. https://doi.org/10.1023/A:1010337215241