12/8/2005

Benjamin Schlein
Harvard University

Derivation of the cubic nonlinear Schroedinger equation from many-body quantum dynamics

We consider a bosonic system of N particles, interacting through a repulsive short range mean field potential. In the limit of large N, we derive macroscopic evolution equations for the dynamics of the system such as the relativistic Hartree equation and the nonlinear Schroedinger equation. This is a joint work with A. Elgart, L. Erdoes and H.-T. Yau.