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Workshop

Error estimates in mean field dynamics

  • Benjamin Schlein (Harvard University, Cambridge, USA)
G3 10 (Lecture hall)

Abstract

In bosonic many body systems described by mean-field Hamiltonians, the time evolution of factorized N body wave functions can be described in the limit of large N by the solution of a nonlinear Hartree equation. More precisely, one can prove that the one-particle density associated with the solution of the N body Schroedinger equation converges, as N tends to infinity, to the orthogonal projection onto the solution to the Hartree equation. Although the difference between the one-particle density and the orthogonal projection can be shown to be of order 1/N for short times, so far it has not been possible to extend this estimate on the error to long times. In this talk I am going to present some preliminary result in this direction obtained in collaboration with I. Rodnianski.

Katja Bieling

Stefan Adams

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Manfred Salmhofer

Universität Leipzig