Bose-Einstein condensates in disorder potentials - What is it and is its simulation reliable?"

Bose-Einstein condensates are formed when a dilute gas of bosons is cooled down to ultra low temperatures close to absolute zero. Such condensates have many remarkable properties, its superfluid character (frictionless flow) only being one of them. As corresponding physical experiments can be very challenging, numerical simulations are a highly desirable alternative. However, can we always rely on the results obtained by such simulations or can it happen that the correct physical solutions are not captured? This question is closely connected to the smoothness of physical solutions, which can be very low if the condensate is for instance trapped in a rough potential.

In this talk I will give a short introduction to the physical phenomenon of Bose-Einstein condensation and its mathematical description. Using this as a starting point, we will discuss possible numerical discretizations and what we can say about their convergence. In particular we will have a look at how much the mathematically necessary assumptions are in accordance with what can be physically justified.