Mathematical Physics Seminar

We consider the three-dimensional time-dependent Gross-Pitaevskii

equation arising in the description of rotating Bose-Einstein

condensates and study the corresponding scaling limit of strongly

anisotropic confinement poten- tials. The resulting effective

equations in one or two spatial dimensions, respec- tively, are

rigorously obtained as special cases of an averaged three dimensional

limit model. In the particular case where the rotation axis is not

parallel to the strongly confining direction the resulting limiting

model(s) include a negative, and thus, purely repulsive quadratic

potential, which is not present in the origi- nal equation and which

can be seen as an effective centrifugal force counteracting the

confinement. This is joint work with Florian Mehats.