M ay 2 00 0 A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-dimensional Bose Gas

@inproceedings{Lieb1999MA2,
  title={M ay 2 00 0 A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-dimensional Bose Gas},
  author={Elliott H. Lieb and Robert Seiringer and Jakob Yngvason},
  year={1999}
}
We consider the ground state properties of an inhomogeneous twodimensional 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 ρ̄a2 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/| ln(ρ̄a2)|. In contrast to the… CONTINUE READING