Quantum dynamics with mean field interactions: A new approach
We propose a new approach for the study of the time evolution of a factorized N-particle bosonic wave function with respect to a mean-field 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 many-particle SchrÃ¶dinger dynamics and the one-particle nonlinear Hartree dynamics. In particular the one-particle density matrix associated with the solution to the N-particle SchrÃ¶dinger equation is shown to converge to the projection onto the one-dimensional sub-space spanned by the solution to the Hartree equation with a speed of convergence of order 1/N for all fixed times.
134
5-6
859 - 870
859 - 870
Springer