国家数学与交叉科学中心合肥分中心报告

报告题目：Mathematical Models and Numerical Methods for Bose-Einstein Condensation

报告人：Prof. Weizhu Bao,  新加坡国立大学数学系

时  间：2015年5月18日    下午4:00―5:00

地  点：东区管理科研楼  365英国上市官网1218室

内容提要：
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 incondensed 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) formodeling 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 numericalmethods 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 BECand to coupled GPEs for spin-orbit coupled BECs are discussed.
Finally, some conclusions are drawn and future researchperspectives are discussed.

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