二维吸引Bose-Einstein凝聚的临界值和稳定性

Critical Value and Stability for the Two-dimensional Attractive Bose-Einstein Condensates

研究描述吸引Bose- Einstein凝聚 (BEC)的二维Gross- Pitaevskii(GP)方程 .从偏微分方程的严格理论出发 ,应用变分方法 ,解析地导出了凝聚原子的临界值 ,这个值与实验结果完全一致 .进一步在这个临界值下 ,证明了基态孤立子的存在性及其轨道稳定性 .这个结果与Einstein的预测完全一致 .

We study the two-dimensional Gross-pitaevskii(GP) equation as a model of attractive Bose-Einstein condensation. By the rigorous theory of partial differential equations and variational arguements, we derive the critical value of condensate particles. And the value is well consistent with the existing experimental data. Moreover with this value we prove that a ground state of the condensate exists and is orbital stable. And the result agrees with the predict of Einstein.