摘要: The achievement of Bose-Einstein condensation (BEC) in  ultracold vapors of alkali atoms has given enormous impulse to  the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. In this talk, I will present a short survey on mathematical models  and theories as well as numerical methods for BEC based on the mean field theory. We start with the Gross-Pitaevskii equation (GPE) in three dimensions (3D) for modeling one-component BEC of the weakly interacting bosons, scale it to obtain a three-parameter model and show how to reduce  it to two dimensions (2D) and one dimension (1D) GPEs in certain  limiting regimes. Mathematical theories and numerical methods for ground states and dynamics of BEC are provided. Extensions to GPE with an angular momentum rotation term for a rotating BEC, to GPE with long-range anisotropic dipole-dipole interaction for a dipolar BEC and to coupled GPEs for spin-orbit coupled BECs are discussed. Finally, some conclusions are drawn and futu re research perspectives are discussed.

    报告人简介：包维柱教授,清华大学数学系本科、硕士、博士(1995)，博士毕业后在清华大学历任讲师、副教授。2005年受聘于新加坡国立大学数学系，2009年晋升为教授。1995年获清华大学林家翘应用数学一等奖；2003年获北京市科技二等奖，2008年获新加坡国立大学理学青年科学家奖；2008获新加坡国立大学理学杰出科学家奖；2013年包教授因其在数值分析玻色-爱因斯坦凝聚和计算Schrodinger方程解的杰出成就获“冯康科学计算奖”；2014年应邀在第27届国际数学家大会上做45分钟报告。包维柱教授研究兴趣包括：玻色-爱因斯坦凝聚态、计算流体力学、双曲型守恒定律、计算量子物理和化学、多尺度建模仿真和应用、无界区域问题的数值方法、数值分析/科学计算和应用数学。近年来，在SIAM J. Sci. Comput., SIAM J. Numer. Anal.,J. Comput. Phys.等国际一流杂志发表论文百余篇。现为Adv. Numerical Analysis, East Asia J. Applied Math., J. Math. Study,Applied Mathematics and Mechanics, Computational Astrophysics and Cosmology, Asian J. Mathematics等多个国际期刊的编委。