|Date:||Wed, September 18, 2019|
|Place:||Research III Seminar Room|
Abstract: We study the dynamics of a system of N interacting bosons in a cigar- or disc-shaped trap, which initially exhibit Bose-Einstein condensation and interact via a non-negative interaction potential in the Gross-Pitaevskii scaling regime. The trap is realized by an external potential, which confines the bosons in two/one spatial dimensions to a region of order $\varepsilon$. We study the simultaneous limit $(N,\varepsilon)\to(\infty,0)$ and show that the N-body dynamics preserve condensation. The time-evolved condensate wave function is the solution of a 1D/2D Gross-Pitaevskii equation. Joint work with Stefan Teufel.