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Quantum Dynamics with Mean Field Interactions: a New Approach

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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 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 Schrödinger dynamics and the one-particle nonlinear Hartree dynamics. In particular the one-particle density matrix associated with the solution to the N-particle Schrödinger equation is shown to converge to the projection onto the one-dimensional 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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Authors and Affiliations

  1. Institute of Mathematics, University of Munich, Theresienstr. 39, 80333, Munich, Germany

    László Erdős & Benjamin Schlein

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  1. László Erdős
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  2. Benjamin Schlein
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Correspondence to Benjamin Schlein.

Additional information

Dedicated to Jürg Fröhlich on the occasion of his 60th birthday, with admiration and gratitude.

L. Erdős is partially supported by SFB/TR12 Project from DFG.

B. Schlein is is on leave from Cambridge University; his research is supported by a Kovalevskaja Award from Me Humboldt Foundation.

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Erdős, L., Schlein, B. Quantum Dynamics with Mean Field Interactions: a New Approach. J Stat Phys 134, 859–870 (2009). https://doi.org/10.1007/s10955-008-9570-7

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  • DOI: https://doi.org/10.1007/s10955-008-9570-7

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