Mathematical Physics Seminar, January 13, 2009

Antti Knowles

The mean-field limit: rate of convergence and singular potentials

It is a well-known fact that the mean-field dynamics of an interacting Bose gas is described by the nonlinear Hartree equation. The mathematical study of this problem has a long history. However, several physically interesting aspects of the mean-field limit have only been considered recently. For instance, one might be interested in tight error bounds, which indicate how many particles are needed for the mean-field approximation to be valid. Another question of interest is the class of external and interaction potentials - especially singular ones such as the Coulomb potential - for which the mean-field description can be proven to be correct. I present some recent work in collaboration with P. Pickl which, among other things, generalises previous results on both aspects mentioned above.