Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics

Details Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics

2007-11-20

arxiv.org/abs/0711.3087v1

Physics

Mathematical Physics

latex file, 29 pages

Scientific paper

The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics. More precisely, we prove bounds on the difference between the one-particle density associated with the solution of the N-body Schroedinger equation and the orthogonal projection onto the solution of the Hartree equation.

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