 0881 Laszlo Erdos, Benjamin Schlein
 Quantum Dynamics with Mean Field Interactions: a New Approach
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Apr 23, 08

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Abstract. We propose a new approach for the study of the time evolution of a factorized $N$particle bosonic wave function with respect to a meanfield dynamics with a bounded interaction potential. The new technique, which is based on the control of the growth of the correlations among the particles, leads to quantitative bounds on the difference between the manyparticle Schr\"odinger dynamics and the oneparticle nonlinear Hartree dynamics. In particular the oneparticle density matrix associated with the solution to the $N$particle Schr\"odinger equation is shown to converge to the projection onto the onedimensional subspace spanned by the solution to the Hartree equation with a speed of convergence of order $1/N$ for all fixed times.
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