Communications in Mathematical Physics

, Volume 225, Issue 2, pp 223–274

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

  • Jürg Fröhlich
  • Tai-Peng Tsai
  • Horng-Tzer Yau

DOI: 10.1007/s002200100579

Cite this article as:
Fröhlich, J., Tsai, T. & Yau, H. Commun. Math. Phys. (2002) 225: 223. doi:10.1007/s002200100579

Abstract:

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear Møller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential Wx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ−1. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential Wx).

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jürg Fröhlich
    • 1
  • Tai-Peng Tsai
    • 2
  • Horng-Tzer Yau
    • 2
  1. 1.Theoretical Physics, ETH-Hönggerberg, 8093 Zürich, Switzerland. E-mail: juerg@itp.phys.ethz.chCH
  2. 2.Courant Institute, New York University, New York, NY 10012, USA.¶E-mail: ttsai@cims.nyu.edu; yau@cims.nyu.eduUS