摘要
Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N｜k｜, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.
Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N｜k｜, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.
基金
supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China,National Center for Mathematics and Interdisciplinary Sciences in China
