# PDE Seminar

## Symmetry Breaking and Collapse in Bose-Einstein Condensates with Attractive Interactions

### 郭玉劲 教授 (中国科学院武汉物理与数学研究所)

#### 2013年4月18日（周四）下午1:00-2:00 闵行校区行政楼12楼PDE中心1202报告厅

Abstract. This talk is focussed on the Gross-Pitaevskii functional describing two-dimensional Bose-Einstein condensates (BEC) with attractive interactions. We show that there exists a positive constant $a^*$ such that the minimizers exist if and only if the attractive interaction strength a satisfies $a< a^*$. This gives equivalently the analytic proof of the critical number's existence for cold atoms in attractive BEC, which was observed firstly in BEC experiments as early as in 1995. We also analyze the symmetry breaking and collapse of the minimizers as a approaches $a^* $(from the left), where all the mass concentrates at a global minimum of the trapping potential $V(x)$.

This is joint work with Robert Seiringer at McGill University.