### Abstract

We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number N is large but ρ̄a^{2} is small, where ρ̄ is the average particle density and a the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional with a coupling constant g ∼ 1/| 1n(ρ̄a^{2})|. In contrast to the 3D case the coupling constant depends on N through the mean density. The GP energy per particle depends only on Ng. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a Thomas-Fermi type functional is adequate.

Original language | English (US) |
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Pages (from-to) | 17-31 |

Number of pages | 15 |

Journal | Communications In Mathematical Physics |

Volume | 224 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2001 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Communications In Mathematical Physics*,

*224*(1), 17-31. https://doi.org/10.1007/s002200100533