Seminars & Colloquia Calendar

Abstract:  We consider the dynamics of N bosons in a mean-field limit in large volume. It is well known that to leading order the N-body Schroedinger dynamics can be approximated by the Hartree equation. This talk is about the Bogoliubov approximation, which is the next-to-leading order correction that also describes the fluctuations around the mean-field Hartree state. While the Hartree approximation gives convergence in the sense of reduced densities, the Bogoliubov approximation gives convergence in the sense of the L^2 norm of the N-body Hilbert space. Here, I will present a rigorous derivation of this approximation in the setting where both the volume and the density of the gas tend to infinity and the interaction is scaled with the inverse density (instead of the inverse particle number). These results can be applied to derive the dynamics of a density perturbation in a large volume Bose gas. In this case the coupling constant is such that the self-interaction of the fluctuations is of leading order, which leads to a finite speed of sound in the gas.

This is joint work with Peter Pickl and Avy Soffer.