Mathematical Physics Seminar

I consider the dynamics of an interacting Bose gas in the
mean-field limit. I outline how one may prove the convergence to the
mean-field limit in the "Heisenberg" picture of observables instead of
the more common "Schrödinger" picture of states. This result may be
interpreted as an Egorov-type semiclassical theorem. Our method works
for interaction potentials with Coulomb-type singularities. Instead of
using Hardy inequalities, we control the singularity using the
dispersion of the free time evolution. In particular, our results are
applicable to L^2 initial data. Joint work with Jurg Fröhlich and
Simon Schwarz.