Yongyong Cai
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SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Yongyong Cai Abstract. Gross-Pitaevskii equation (GPE), also known as the nonlinear Schroedinger equation (NLSE), is a widely used model in different subjects, such as quantum mechanics, condensed matter physics, nonlinear optics etc. In this talk, we will focus on GPE with applications in Bose-Einstein condensation (BEC). BEC was predicted by Bose and Einstein in 1924-25, and eventually realized in experiments in 1995. The physicists, E. Cornell, C. Wieman and W. Ketterle were awarded Nobel Prize in physics 2001 for their achievements in BEC experiments. Since then, GPE has regained considerable research interests due to the experimental success of BEC, which can be well described by GPE at ultra-cold temperatures. In the talk, I will first review properties of BEC and GPE. After that, we focus on the GPE with dipole-dipole interaction modeling degenerate dipolar quantum gas. The two important issues in the study of BEC, the ground states and the dynamics, will be discussed. Then we will talk about dipolar BEC in lower dimensions. Both mathematical results and numerical studies will be presented. At the end of the talk, some interesting and important future research topics will be addressed. |