Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators

Mathphys Analysis Seminar

In this talk I will present a new derivation of the time-dependent Gross-Pitaveskii equation from a system of interacting bosons in $\mathbb{R}^3$. Our derivation is based on a simple Gronwall estimate for suitably renormalized excitation number operators and yields optimal convergence rates. I will conclude the talk with some related open questions on the quasi-free approximation of the many-body dynamics. The talk is based on joint works with W. Kroschinsky and B. Schlein.